I suppose we have to realise that all these characters are not historians. They may not be reliable narrators. McCoy is a doctor, not a historian.
Admiral Bennett in 'Dr Bashir, I Presume?' may be the one with a faulty knowledge of history! (Ron Moore is off the hook!)
I mean, in daily life, people don't often go around talking about specific historical events (which goes some way towards explaining why they never mentioned Jonathan Archer in TOS, TNG, DS9, or VOY; there was no need for them to). And when people do talk about history, unless they're an expert in the field, there's often a bit of generalisation involved, and an amount of incorrectness.