This idea is a riff on constrained writing, where certain things are forbidden or a pattern is enforced. One of my favorites examples is haiku: you're constrained to write a poem three lines long in a 5-7-5 syllable pattern.
The Bible study was constrained theology because when we were talking about how Paul didn't get his faith just from a vision I couldn't bring up Alma 5:46. When we discussed how we receive inspiration I couldn't bring up D&C 9:8. And so on.
But of course, that didn't mean I couldn't participate, I just had to constrain my scriptural citations to the Bible. It reminded me of James Talmage in Jesus the Christ--he didn't have the Joseph Smith translation available to him (or at least he didn't trust it if he did--the LDS church was worried the RLDS church might have made alterations to the manuscripts when they published it) so he had to deal with all the tough passages in the New Testament as they were. He ends up doing a wonderful job interpreting them honestly and persuasively, but his understandings are now somewhat obsolete because we now just look at the JST footnote and don't struggle over those hard passages. But the point is that because Talmage was constrained, he wrestled with the tough questions and still came out on top. I fear that we look today too easily to "easy" answers that clean up all the possible contradictions or paradoxes in scripture, the JST being just one small example*.
I believe there's a lot of value in the wrestle. Constraining myself to using only the Bible to support my views was a good time to remember that. There are still tons and tons of examples to be drawn from the Bible to answer the questions I mentioned above, but because there are such pat answers in other scriptures we Mormons tend to overlook them. It was great to look at the Bible in a new and more independent light last night and remember that there's a lot of answers in there that I don't know as well as the answers I know in the Book of Mormon and D&C. Hopefully I can work on getting to know all scriptures better and also remember not to let a simple answer be the end of a difficult question.
* Not that I'm against using the JST, but I think it should be one factor to be weighed in understanding a verse, not a complete replacement for the original verse we have.