You're begging the question. You started with: assume there is a factual past of where you were. And then argued: there is a factual past.

I'm not enough of a skeptic to say "don't trust the models of the past"; memory turns out to be a pretty good model. So does carbon dating.

But the reason you say "you were not there and did not commit the crime" is because you don't remember being there. Maybe you even remember being elsewhere. But that doesn't mean it's true, memory is fallible.

You might say that you even have photos of yourself somewhere else at the time. But if there were photos of you at the crime scene, would that change what the past was? Maybe your memory is shoddy, or maybe the photos are fake.