At least in that case, we saw his face. No, canonically we don't know for certain that it's McCoy, but given the evidence we have -- his appearance, his dialogue -- the hypothesis that it is Leonard McCoy has a very high probability
. Conversely, we have no canonical evidence to suggest that Jonathan Archer living to a record-breaking age is more probable
than Jonathan Archer having heirs who also went into Starfleet and liked beagles. The latter is far more likely to be true.
This is how you decide between different possibilities. Very few things in life are matters of absolute certainty. There's always room for doubt, and there are a lot of things that you can't know directly and have to deduce from limited evidence. So the thing to do is to think about the options in terms of probability
. You pick the interpretation that's most likely, that's the best fit to the available evidence and to your understanding of the world in general. And you don't favor a far less probable option over a far more probable one unless you have solid evidence to back it up. As Carl Sagan said, extraordinary claims require extraordinary evidence. They're the ones that the burden of proof lies on. So I'm not going to believe an extraordinary claim like Jonathan Archer living that long unless I'm presented with proof.