I found this little tidbit on line, which attempts to address my question.
Just before his death Joseph Smith, also with prophetic perception, wrote, "By proving contraries, truth is made manifest" (History of the Church, 6:428). By "prove" he meant not only to demonstrate logically but to test, to struggle with, and to work out in practical experience. The Church is as true — as effective — as the gospel because it involves us directly in proving contraries, working constructively with the oppositions within ourselves and especially between people, struggling with paradoxes and polarities at an experiential level that can redeem us. The Church is true because it is concrete, not theoretical; in all its contradictions and problems, it is at least as productive of good as is the gospel.-- Eugene England
I don't know that I can agree with either Eugene England or Joseph Smith. Groking (meditating) is.......
Then I came upon this:
Then I stumbled onto the medieval doctrine of twofold truth, discussed briefly in this Catholic Encyclopedia entry on Averroes (third paragraph down). In a nutshell, the doctrine holds that what is false in philosophy can, at the same time, be true in theology, and vice versa. Here's a quote from the article:
Averroes advocated the principle of twofold truth, maintaining that religion has one sphere and philosophy another. Religion, he said, is for the unlettered multitude; philosophy for the chosen few. Religion teaches by signs and symbols; philosophy presents the truth itself. In the mind, therefore, of the truly enlightened, philosophy supersedes religion. But, though the philosopher sees that what is true in theology is false in philosophy, he should not on that account condemn religious instruction, because he would thereby deprive the multitude of the only means which it has of attaining a (symbolic) knowledge of the truth.
This probably rubs you the wrong way; the doctrine of twofold truth hasn't fared well in the modern era. However, it strikes me as similar to compartmentalization, a standard coping technique of educated Mormons when faced with contrary claims between religion and science, such as Book of Mormon claims about Israelites/Nephites in America versus the disturbing lack of archaeological evidence for that claim. Solution: compartmentalize. Averroes apparently advocated a sophisticated formulation of compartmentalization. For what it's worth, medieval Scholastics rejected that approach: Scotus and Aquinas would have none of that two truths stuff. Truth was truth and had to be consistent, even if there were two roads (natural reason and divine revelation) to get there. "Truth brooks no contraries" might be their slogan.
How about just "Pondering Contraries?"--- Some guy named Dave on the internet.
My gut tells me that we all have about the same access to the "divine" but we interpret it differently, based on our experiences and innate abilities. Takes me back to the "Six blind men and the Elephant." Which might be a good metaphor for Church leadership.

God is Love. God is Truth. The greatest problem with organized religion is that the organization becomes god, rather than a means of serving God.