A while ago, I read this academic paper by Casey Schutt. Although the entire paper was about evangelism ethics in the workplace and how self-identified evangelical/born-again Christians go about doing that in contrast to the religiously pluralistic workplace environment, I got a little interested in how Casey Schutt could just visit a Baptist church and teach 3 different classes. What are the requirements for a teacher in the Baptist church? How trained are they? Do you have to be baptized under the right formula to teach?
One of the key distinctives of Baptist churches is that they are congregationally governed and generally non-creedal. That means there's no overriding "Baptist" policy on who can and cannot teach in the church. You can be fairly certain that most Baptist churches will require a person to have been baptized as an adult in order to teach, but there are exceptions even to that. It's up to the individual church, and usually would be specified in the church's bylaws (or, if not, up to the discretion of the pastoral staff).
This isn't to say that Baptist churches are universally lax about who can teach, only that their standards aren't unified. Besides baptism, the typical requirements would be based on 1 Timothy 3 and similar passages, which hold leaders to high moral standards and require a certain level of respect and standing within the community.
Some of the more conservative Baptist churches would also exclude women from all teaching roles except that of teaching children. This is becoming less and less common, as even those churches that exclude women from the ordained pastorate often will permit them to teach in some capacity. Of course, many Baptist churches also fully affirm women in pastoral ministry. Again, it's up to the congregation.
You seem to be laboring under some misconceptions about the Baptist church. We Baptist do not believe that ours is the only faith which will wind up in heaven, nor do we believe that we are the only ones which worship the true God.
Not just anyone can teach, nor can just anyone preach in a Baptist Church, even though we do occasionally invite some Christian authorities to give instruction to some of our members, and they may not be Baptists but are well known Christians.
As an example we might have a professor of Theology, teach a class on salvation, to a group of youth. However, he would have to present some kind of credentials, and his lessons would most definitely have to be approved either locally or at some higher level.
We do also from time to time have a guest who has a peculiar witness to tell our congregations of their experience, a process which we know as witnessing.
As far as the article you quoted please give us a page number citing the incident so that we can check it out for ourselves. Also as I read the paper it is about Evangelism, and few Evangelists are limited to a particular Church. Evangelism is all about giving the path of salvation to the unsaved, and is generally accepted as nondenominational.
Baptists are happy to welcome anyone to their services in hope that the Holy Spirit will touch the heart of someone who needs it. after all Jesus said:
Mark 2:17 When Jesus heard it, He said to them, "Those who are well have no need of a physician, but those who are sick. I did not come to call the righteous, but sinners, to repentance."
In most of the Baptist churches I have attended the purpose of the sermon is to explain the word of God to the members and allow the Holy Spirit to do the calling. Very few services do not end with an Alter call, where those seeking salvation are given that opportunity. Even many Sunday school sessions end that way, and if the message that someone not a member of the Church is evangelistic we would certainly welcome any accredited Christian teaching the way to enter the Kingdom of God.
Baptist services are a celebration of God's grace and we welcome all who desire to celebrate with us regardless of their denomination. Nor do we discourage people from choosing any other denomination. The God we serve would never deny Heaven to anyone by saying even though you trusted my son for your salvation you cannot enter because you chose the wrong denomination.
John 3:16 in the New King James translation, says:
For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.
And nowhere in the Bible will you find any Denominational requirement.
You can learn about the curriculum and lessons published for Baptist Sunday school teachers which are designed so that they can be taught by laymen at the following web site http://www.lifeway.com/n/Bible-Study/Sunday-School-Groups?CMPID=Adwords-lifeway%20sunday%20school%20lessons_sunday-school-lessons&s_kwcid=AL!4443!3!26284083117!e!!s!!lifeway%20sunday%20school%20lessons&gclid=CPXXh-343cMCFYNDaQodFm0ArQ&ef_id=VM1RrQAABMp7ojeb:20150213030839:s
Hope this helps.