Everybody believed that when Craig Wright made his wrong cryptographic proof he was cheating. But this was a deliberate hoax, making a fool of us all.
The video
https://www.youtube.com/watch?v=FIvqn87iAz8 reveals it all (but apparently nobody understood what he was saying):
One needs to look at the message he claimed to sign but didn't sign:
" Wright, it is not the same as if I sign Craig Wright, Satoshi.\n\n"
which was a variant of the message by Sartre by which he refused to take the Nobel prize:
It is not the same thing if I sign Jean-Paul Sartre or if I sign Jean-Paul
Sartre, Nobel Prize winner. A writer must refuse to allow himself to be
transformed into an institution, even if it takes place in the most honorable form."
So in essence he was a saying: If I sign the message that I'm Satoshi, then I betray myself because then I'm no longer the person I was before. I refuse to sign.
So he didn't cheat because he didn't have a key, but because it is against his anti-authoritarian conviction.
This doesn't prove of course that he has the keys, and doesn't prove that he is Satoshi Nakamoto, but for me the mindset this is coming might indicate he may indeed be Satoshi Nakamoto.