One could also point out the the underlying assumption of the question seems to rest on LLMs as representing “just statistics on language”, which is only a correct assertion insofar as babies learn language by just doing statistics on language. I am at this point not even sure what people think they mean when they say this, what they think these “statistics” are, and why they think calling the system “statistics” instead of “cognitive algorithms” does any philosophical work.
In other words, the OP seems to rest on the framing that LLMs are “just” doing “statistical analysis” that this is some kind of meaningful distinction, as if the argument would change if LLMs were doing some other kind of analysis.
I can’t escape the sense that I am being overly generous and that the OP simply has no idea how transformers or even neural networks work, but feels very sure that it must be some kind of parlor trick, and thus presumes that it is so.