Indeed, this has been the most contentious line in the whole piece :D

How do you define "perfect" data and training? I'd argue that if you trained a small NN to play tic-tac-toe perfectly, it'd quickly memorise all the possible scenarios, and since the world state is small, you could exhaustively prove that it's correct for every possible input. So at the very least, there's a counter example showing that with perfect data and training, models will not get stuff wrong.