I think many humans engage in metacognitive reasoning, and that this might not be strongly represented in training data so it probably isn't common to LLMs yet. They can still do it when prompted though.
Funny, because "post-hoc rationalization" is how many neuroscientists think humans operate.
That LLMs are stochastic inference engines is obvious by construction, but you skipped the step where you proved that human thoughts, self-awareness and metacognition are not reducible to stochastic inference.
AI most certainly has nothing of the sort, and any appearance to the contrary is the direct result of training data.