You're conflating accuracy with engine correlation. Having a perfectly accurate game means you didn't make any moves that caused a centipawn loss. Having 100% engine correlation means you're making the exact moves the engine would make.
I think I have on 3-4 occasions played a game where, after evaluating on chess.com, got a 100% accuracy (which is engine correlation). A couple times were all theory and then blundering a mate in 1, but...
I did have one game where I didn't know the theory except a very vague recollection in the beginning. I actually thought I had blundered in that game and was trying to figure out what I'd do if my opponent made a certain move — they didn't find it, I ended up winning material in a tactic and they resigned — I was in complete shock when it came back 100% accuracy (and I definitely did not see the engine response to the move I was worried about, which was the best move).
I'm only around 1600-1700 on chess.com.
Not taking a position either way on Hans, but I have no doubt he knows far more theory than I do (and I do know some lines 20+ moves deep), and correlating with an engine is not impossible even outside of book.
To repeat what was said above, accuracy is not the same as engine correlation.
Engines often play moves that are counterintuitive and weird, but nonetheless good. This is because they can evaluate large trees of tactics in a way that humans cannot.
If a human finds a natural move that is just as good as the engine move (in terms of evaluation), they are still playing accurately, but they are uncorrelated with the engine. Playing accurately is not a sign of cheating. Playing many engine moves is a sign of cheating.
The engine scores centipawn loss against the perfect move (according to the engine). The engine plays the move with the lowest centipawn loss itself. How are those two different?
