If he was though, it'd have various implications such as it not being difficult to prove he had access to his own private keys.

I can imagine you might be the guy and not want to prove it, or it to be known. But actively claiming to be the guy and not proving it indisputibly when you could... what'd be the point?

Besides having private keys to early wallets, my #1 reason to not believe him is his arrogance and loving attention. The Nakamoto(s) that wrote the white paper and spoke on forums about it was/were very anonymous and privacy-obsessed.