It is true that LLMs often behave haphazardly, and do rely on statistics. But plenty of research has shown them behaving in methodical ways too. There are findings going both ways!
Granted, many of the strongest contradictory results appeared after the Stochastic Parrots paper, so it isn't like they were ignoring the literature at the time. But they did make a very strong claim, and in the half-decade since, a lot of evidence has come out against it.