You can train LLMs on the output very complex CFGs, and it successfully learns the grammar and hierarchy needed to complete any novel prefix. This is a task much more recursive and difficult than human languages, so there's no reason to believe that LLMs aren't able to parse human languages in the formal sense as well.
And of course empirically LLMs do generate valid English sentences. They may not necessarily be _correct_ sentences in a propositional truth-value sense (as seen by so-called "hallucinations), but they are semantically "well-formed" in contrast to Chomsky's famous example of the failure of probabilistic grammar models, "Colorless green ideas sleep furiously."
I'm not a linguist but I don't think linguistics has ever cared about the truth value of a sentence, that's more under the realm of logic.
And of course empirically LLMs do generate valid English sentences. They may not necessarily be _correct_ sentences in a propositional truth-value sense (as seen by so-called "hallucinations), but they are semantically "well-formed" in contrast to Chomsky's famous example of the failure of probabilistic grammar models, "Colorless green ideas sleep furiously."
I'm not a linguist but I don't think linguistics has ever cared about the truth value of a sentence, that's more under the realm of logic.