1) LLM's written CoT might not always be faithful to the model's real reasoning process (true and important)
2) The "stochastic parrot" hypothesis, which the article reintroduces as "approximate retrieval" - ie, LLMs don't "really reason" at all, they just memorize a lossy encoding of their training data. This obviously raises the question of how LLMs can now routinely solve open mathematical problems, with no solutions in the training data by definition. The article handwaves this with:
"The model doesn’t have to learn or reliably apply a general reasoning process, Kambhampati said; it just has to absorb enough examples of what the steps look like to predictively mimic them on its way to “stitching together” a plausible result that can then be verified."
The problem is that "mimicking" training data to arrive at a "plausible" result gets you an incorrect-but-plausible-sounding "proof" of the Jacobian conjecture, which was famous for humans writing plausible-looking "proofs" that had subtle flaws. You can't disprove the conjecture through sheer luck (search space too large) or "approximate retrieval" (the only thing you'd retrieve are fake "proofs"; far more human effort went into proof than disproof) or by writing something "plausible" that just happens to be correct (Jacobian was famous for "plausible" but wrong); the model must be carrying out mathematical reasoning somehow, by any sane definition of the word, even if it isn't fully reflected in CoT. The article doesn't address this.