Does she preach the basic Christian message of salvation by faith in Jesus alone.
No.
Allow me to explain.
Another answer has postulated "yes", and there is a sense in which there are words she uses that can be construed that way. The trouble is most of them can also be construed another way. It is therefore necessary to look at the broader context of her teachings in order to determine how well they align with a "salvation by faith in Christ alone" Gospel.
This is a tricky issue because she mixes and matches a lot of content. Taken in isolation some, indeed many, points of her doctrine may seem in agreement with mainstream Christian teaching. It isn't until you put all the pieces together that you see the pieces fit in a different puzzle.
Definition of terms and outline of scope
In order to treat an open-ended question like this on this site, I think it is necessary to identify who holds what views and who, exactly, has issues with what. For the purposes of the scope of this site, anyone self-professing to be Christian is on topic. Baring any further scoping (which your question is a bit thin on) I will be working under the assumption that you are questioning from a generic mainstream Protestant perspective.
Since it seems self evident that this question isn't directed at Catholicism or Orthodoxy and the (dubious) tag biblical-basis tends to be the focus of Protestants, I'll be tackling this from that direction.
Broadly I find the following conflicts between Joyce's teaching on salvation and "salvation by faith".
- She defines the concepts of faith and works differently.
- She defines salvation differently.
- It isn't her main message.
Statement of faith
If you examine the statement of faith from her website, there isn't much there to cause alarm. Most of it could pass for most any non-denominational or even Baptist. There are a couple of items that put it in a more Pentecostal camp, maybe most similar to AOG.
The trouble is the statements there are not consistent with what she teaches. For example point 1:
The Bible is the infallible Word of God, inspired by the Holy Spirit, and contains every answer to man's problems.
Sounds good. The trouble is she doesn't actually hold to the sufficiency of Scripture doctrine held by mainstream Protestants. Instead she believes in continued special revelation. She teaches that some things Christians should know are not spelled out in the Bible.
The Bible can’t even find any way to explain this. Not really that is why you have got to get it by revelation. There are no words to explain what I am telling you. I have got to just trust God that he is putting it into your spirit like he put it Into mine. — Joyce Meyer (audio clip)
In other words, her statement of faith is not an accurate guide to her teachings. Ergo when it comes to the part relevant to your question, we must examine whether the statement is actually reflected in her teachings.
Man is created in the image of God but separated from God by sin. Without Jesus we cannot have a relationship with God.
We can have a personal relationship with God through salvation, God's free gift to man. It is not a result of what we do, but it is only available through God's unearned favor. By admitting we have sinned and believing in the death, burial and resurrection of Christ, and accepting Him as Lord, we can spend eternity with God.
Alright so we have some stuff about Jesus, sin, salvation, personal relationship, etc. Fair enough.1 Lets see how they play out.
Soundly Biblical?
Your question made this observation:
I only saw one talk and it was soundly Biblical.
This analysis would be is widely disputed by mainstream Protestants. See for example CARM's analysis.
So lets break down to where the dispute lines fall:
Starting easy, cults such as LDS and JW are different enough on core issues that no comparability is either implied or assumed.
The structure of Catholic, Orthodox, and even Anglican churches differs enough from her independent organization of one that there isn't much question that they don't match up.
Mainstream Protestants with which she is most often assumed to be associated (due in main part to her self-identification af 'simply Christian' have repeatedly disavowed her (some of the reasons for such are will be covered below).
Doctrinally, there are some notably similarities with the Seventh Day Adventist Church. Her view of continued revelation is not that different from the role Ellen White plays in the SDAC. Her views on the relationship between salvation and sanctification are also similar. Notably different would be their views on hell where Joyce is fairly traditional and the SDAC is decidedly Annihilationist.
So who does she agree with? The theological school of thought with which she is most properly identified with is:
It is important to note that when I say "properly identified", I am referring to general theological constructs. She is not officially part of any movement or denomination. Her FAQ, for example, skirts the issue a bit by agreeing with the general teachings while noting awareness of a common point of criticism.
13. Is Joyce Meyer Ministries a "word of faith" ministry?
Joyce Meyer Ministries believes in the Word of God. Joyce teaches that God has made promises to us in His Word and as believers, we should trust His promises. However, it can be damaging when people place their faith in faith alone instead of placing their faith in God. Misappropriation of God’s promises solely for personal gain is not scripturally supported.
While most adherents don't use this terminology, Joyce is firmly in the realm of what mainstream Protestants would call 'Prosperity Gospel' or 'Health and Wealth'. Note what Wikipeda gives for references. This distinctive is even openly claimed in her FAQ, albeit with the same caveat as for Word of Faith, noting a weakness of the movement.
14. Does Joyce Meyer Ministries teach a "prosperity gospel"?
Joyce Meyer Ministries believes that God desires to bless His people. Joyce teaches that God’s blessings and prosperity apply to the spiritual, emotional, physical and financial areas of life. These blessings and prosperity are then to be used to bless others. A "prosperity gospel" that solely equates blessing with financial gain is out of balance and could damage a person’s walk with God.
In any case the overwhelming majority of her teaching falls squarely in this camp, and her choice of associations brings that tie even closer. See appearances with T.D. Jakes (former Oneness Pentecostal, + Word of Faith), her citations of Benny Henn (on the short list of top Prosperity Gospel proponents) on humans being 'little gods', sinlessness, etc., etc.
If you consider Prosperity / Health & Wealth teachings to be "soundly Biblical", the following may or may not be points of concern for you, but they are certainly causes for concern for mainstream Protestants of many different denominations.
So does she teach salvation by faith?
In addition to my previous knowledge and studies, in preparing for this answer, I reviewed about 3.5 hours of Joyce's teaching: 2 long conference segments and a few shorter messages (but still in whole segments so I'm sure I'm not just working with somebody else's cherry-picking. There are a couple of things to not from such a sampling.
While "faith" is often mentioned in her teachings including in the context of salvation, the fact that salvation if by faith alone is never stressed in the way that the Protestant doctrine of sola fide would have it be.
Works are never mentioned as a means to salvation, but they are constantly mentioned as a means to everything else. Her teaching is riddled with stories, often of her own experiences. The vast majority of these follow a pattern of "struggle with x, then finally I did y" or "make x mistake, then I realized y and did z". From a pragmatic standpoint a lot of preachers messages will include talk like this from time to time, but Joyce's preaching is exceptional for the pervasive use of the "I did" pattern. It is classic self-help coaching. God doing things and changing people is hardly given mention expect in response to something that men do first. All his action / blessing / etc is done as a result to somebody else's actions.
Here is a direct quote I heard in multiple sessions speaking to that theology:
If we do things God's way God will give us double for our trouble. — Joyce Meyer
The scenario is constantly 'we do x, then and only then does God step up to do y'.
Her concept of "salvation" is at variance with Protestantism on the issue of sanctification.
In Protestant theology, we are saved from sin and justified before God once and for all by means of Christ's propitiatory death. Of the various pieces that make up salvation, justification happens once and for all but the process of our sanctification as believers is underway but not finished yet. Joyce completely disagrees with this and believes that as a result of her salvation she does not sin.
I am not poor. I am not miserable and I am not a sinner. That is a lie from the pit of hell. That is what I were and if I still was then Jesus died in vain. I'm going to tell you something folks. I didn't stop sinning until I finally got it through my thick head I wasn't a sinner anymore. And the religious world thinks that's heresy and they want to hang you for it. But the Bible says that I am righteous and I can't be righteous and be a sinner at the same time. — Joyce Meyer (youtube source)
If the context of the Protestant doctrine of salvation my faith alone, the 'not by works' clause is a necessary clarification because we believe we are still sinners and, even in our 'saved' state we continue to sin. Hopefully we are learning to recognize sin, repent from sin, etc. We are in the process of putting sin to death, but it hasn't been completely purged from us yet. That's the ongoing process of sanctification that will not be completed until we are taken up to glory in Chris's presence. Ergo if our salvation depended on our works we would fail. We continue to sin and grieve God even as his adopted children.
In contrast the clause 'not by works' is basically meaningless for Joyce because she believes she is no longer a sinner and does not sin. So whether her salvation depended on works or not is no longer a meaningful distinction. She is correct in identifying that most of the religious world (by which I assume she means "Christian" world) believes this to be heresy.
Somebody who believes they can be / are currently sinless in our earthly pre-glorification state cannot be said to preach "salvation by faith" in the same way other Protestants do because she means something different when she says 'salvation'. To her credit she does teach a fairly orthodox view of hell and that we are saved from it by Jesus having gone there in our place2, but again very little airtime is given to the work of Christ in her teachings, most of it is human focused, self-help-ism.
In nearly well over 3 hours of whole segments, the amount of time she spent making any remarks on salvation at all was less than 5 minutes sum-total.
Can it properly be said that someone who does not devote any attention to a subject at "preaches" it per your question? I think not. She does not "preach" salvation an all. Her attention is solely on other matters.
Given that her professed ministry focus is to believers, is this appropriate?
Reading the apostolic letters to the NT churches addressed to believers, the amount of focus placed on salvation and how it works is much higher. I havn't done the statistics but my gut level instinct based on reading and preaching the NT is that it's closer to 1/3 that 1/50.
Most of Protestantism places a high value on the fundamentals of salvation in Christ, giving it regular airtime even to audiences that are assumed to be mostly Christian.
Conclusion
The specifics of your question boil down to this:
Does Joyce Meyer use a lot of words and phrases that sound familiar to evangelical ears? Sure.
When she uses there words, does she mean the same thing by them as is meant by most Protestants? Clearly not.
So can it be claimed that she "preaches salvation by faith" when a) none of the other pieces of her doctrine fit the puzzle that sola fide came from and b) most of what she preaches is something else entirely that is at fundamental variance with what sola fide brings with it doctrinally? No. She does not preach a gospel and a salvation that is consistent with "And this is not of yourselves, but it is the gift of God;".
End note regarding your comment about translations:
Quoting from the Amplified version which seems to be her preference.
Interesting that you should note this. There is nothing inherently wrong with the Amplified version and it certainly serves a purpose. However, extensive reliance on it in teaching is a signal that there may be hermeneutical problems with the message. It can be useful in identifying the inherent difficulty of mapping Biblical languages to English and for getting your head around the possible senses of a text, but it does not help you settle on which sense(s) were intended and or guide correct interpretation. If not combined with other good hermeneutical practices, it leaves the text open to possibly saying much more (or quite different) things than it should rightly interpreted to say.
This tends to make it a favorite by teachers who don't actually have another hermeneutical leg to stand on. The Amplified translation, while a good tool used properly, in this scenario becomes a convenient spring-board for making a passage say whatever a speaker wants it to say. In the case of Joyce Meyer, she makes no bones about the fact that she does not believe the words of Scripture alone are sufficient to understand God's message and that she believes she has a special anointing to do explain things beyond the words of Scripture.
1 Actually not fine, my Reformed inclinations also want to point out the issue with "by admitting" being made causative rather that being a result of God's work in changing hearts, but for the body of my answer I am trying to stick to a generic Evangelical viewpoint.
2 Most Protestants would again disagree with her on the exact mechanics of this as they believe the wrath of God was poured out on Christ while on the cross, not later in hell. Whether or not (and why) Christ spent time in hell is not universally agreed on, but that the thing he did in our place was completed on the cross is generally agreed on, which Meyers rejects.
