It almost doesnt matter what your theory of language is --- any even plausible account will radically depart from the above statistical model. There isn't any theory of language which supposes it's an induction across text tokens.
The problem in this whole discussion is that we know what these statistical models are (models of association in text tokens) -- yet people completely ignore this in favour of saying "it works!".
Well "it works" is NOT an explanatory condition, indeed, it's a terrible one. If you took photographs of the night sky for long enough, you'd predict where all the stars are --- these photos do not employ a theory of gravity to achive these.
LLMs are just photographs of books.
There's a really egregious pseudoscience here that the hype-cycle completely suppresses: we know the statistical form of all ML models. We know that via this mechanism arbitrarily accurate predictions, given arbitrarily relevant data, can be made. We know that nothing in this mechanism is explanatory.
This is trivial. If you video tape everything and play it back you'll predict everything. Photographing things does not impart those photographs the properties of those things -- those serve as a limited assocative model.
In short, there's no evidence that being in the world makes our knowledge any different from an LLM. The main advantages we have at the moment are sensory learnings (LLMs are not good at comparing smells and flavors) and the ability to continuously train our brains.