However perfect the inner part is, it is not the same as the historic event because the historic event did not have the outer part.
False. The outer part is irrelevant to the inner part in a perfect simulation. The outer part can exert no causal influence, or you won’t get a perfect reply of the original event’s presumed lack of outer part.
There is also the issue that in some cases a thing’s history is taken to be part of it identity.
A thing’s history causes it. If you aren’t simulating it properly, that’s your problem. A perfect simulation of the Mona Lisa was in fact painted by Leonardo, provable in all the same ways you claim the original was.
Unless he’s in the Avatar State, an Avatar is not a native to the other modes of thinking outside his own element. He is aware of them, and can purposefully invoke them once he’s been trained, but they are not ingrained and reflexive. The Avatar State is a (hopefully) friendly (to you) AI, drawing upon the history and knowledge and personal ethical injunctions and methodologies of all past Avatars. And it renders its verdicts with terrifying efficiency and callousness without explanation to those watching.