I've never heard the term 'Bible Christian' before, but I'll roll with this one. It's a really interesting question. Because of the generally vague nature of the question I don't think it's fair to answer on behalf of anybody but myself and a handful of others that I know personal. Lets start with a couple statements of what I believe:
I do believe in Sola Scriptura, meaning that God's word in the form of our written Scriptures is the only and final authority on doctrine. Not nearly enough Christians take the word seriously from beginning to end, examine how it fits together as a whole, and apply it as written to their lives.
I do not believe in personal interpretation, meaning that humans are not allowed to take the scriptures and squash them around like spineless jelly until they fit whatever mold they aproached them with. Far too many Christians treat reading their Bible as an exercise in Humpty Dumptyism.
With those in mind, the issue of paraphrasing is a complex one. I would suggest that the example you gave of quoting a bit of a verse in the closest form that came to mind is acceptable, and even desirable. We should seek to communicate on a natural level with people, and the more scripture that is laced into our conversation, the sounder it is likely to be.
On the other hand, the danger exists that we are misleading folks, pulling things out of context and construing them to mean something they don't. Because of this I think it is important we give references and encourage people to read the real thing. The end goal should always be directing people to God's words, not ours. They should never just take our words for anything.
If/when we do paraphrase, we must make a good-faith effort to be faithful to the meaning and context of the original text and have the intent of funneling people to God's word rather than to our words. We must be open to correction: if a paraphrase we use is demonstrated by a brother to not be an accurate representation of the Word, we must repent and fix our phrasing.
Lastly comes the issue of paraphrase translations. These, I think, can be bad. They serve a purpose certainly, and are interesting to have around to read and inspire thought and application, but they should be approached in the same way that you listen to somebody's sermon: as one persons interpretation of a text that you then need to study and apply yourself. While purely paraphrased translations may have their purpose, they are far too often used as an excuse to put less effort into studying the word.
Is it distasteful? It can be beautiful and it can be ugly. It depends on the context.