Last month I asked Believing Thomas this question

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Could you tell me where you got that information from - that the canon was chosen at the Council of Nicea??? I am really curious. Do you have a quote from somewhere?? What book or source did this come from??

My suspicions of this being myth were confirmed when I stumbled on this article today by James White. He was having the below conversation with some Mormons. The Mormons conversation is exactly what my father-in-law told me a couple of years ago. This is just plain wrong information about this Council of Nicea and I've heard it and read it just too many times like it is "fact". Apparently James White has heard it too many times too.

Quote from James White's article:

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The conversation intensified quickly. "You can't really trust the Bible," my Latter-day Saints acquaintance said, "because you really don't know what books belong in it. You see, a bunch of men got together and decided the canon of Scripture at the Council of Nicea, picking some books, rejecting others." A few others were listening in on the conversation at the South Gate of the Mormon Temple in Salt Lake City. It was the LDS General Conference, and I again heard the Council of Nicea presented as that point in history where something "went wrong," where some group of unnamed, faceless men "decided" for me what I was supposed to believe. I quickly corrected him about Nicea -- nothing was decided, or even said, about the canon of Scripture at that council.1

Here's the rest of the article titled "What Really Happened at Nicea?" by James White http://www.equip.org/free/DN206.htm