Read 1984. How many of the differences were legitimate, and how many were Empire-sanctioned revisions? The MU split could have begun at First Contact, and anything saying otherwise could be propaganda.
True. But if we accept that, how sure can we be of the truth of many statements given by prime-universe Federation or Starfleet members ?
I mean, the prime universe Federation is supposed to be benign, but I certainly wouldn't put propaganda and less eye-catching history revisions past them. Even today western societies espouse very similar values like open access to information, free speech, and such, and there
still is a significant amount of these things going on in our own societies ...
Since I really don't like that possibility, I choose to accept their statements,
and those of the mirror universe, as true. In fact, I think it is a completely different universe, not a deviation from "our" timeline at some point.