That's exciting about the B.U. course, Elizabeth! I hope it's all you were looking for, and more.
Regarding 'the best information," my main concern is that, rather than presenting qualitative assessments of our information, we should say where our information came from. It should be understood that not all "facts" are going to meet the stringent standards of an entity like the Mayflower Society, and that many profiles are going to be based on some form of "best available information," but that "best available" information might have a number of different types of origins. Maybe it's family tradition of the Thayer family, as documented by [Author] in an 1886 book, or maybe it's a situation where several people named Thayer recorded in Taunton are inferred to be from this particular set of parents because that couple were the only Thayer adults of the right approximate age believed to be in Taunton at the right time. Those are examples of just two different types of information that might be called "best available," and that I think need to be distinguished.
In recent visits to museums and historic sites in England and the United States, I've noted with interest that more than a little of the historic information is based on tradition rather than records (e.g., a sign might say "...is thought to be the site where..."). If the historians associated with highly respected museums and historic sites can communicate history without pinning down every detail, it does make us genealogists look absurdly nitpicky when we insist on trying to find baptism and marriage records for every obscure individual person in our ancestry. However, I think that the historians who create narratives for museums insist on knowing what the stories they tell the public are based on. It's just that they don't communicate all of the details in their public exhibits because it would interfere with the narrative and would bore most of the audience. Genealogy has a bad legacy of people blandly accepting -- and republishing -- nicely written family history stories without having a clue where the data came from, with the result that utter garbage (including out-and-out fraudulent pedigrees) sometimes gets propagated. To get past this, modern genealogists are insisting on knowing where our information comes from (as a good historian would), rather than simply accepting nicely told stories and well-drawn pedigrees because they come from somebody who seems to know what they are doing.
I have no objection to sharing this conversation with the museum folks. (Note that the conversation is already on the public Internet!)