I suppose that current LLMs are incapable of answering such questions by saying "I don't know". The have no notion of facts, or any other epistemic categories.

They work basically by inventing a plausible-sounding continuation of a dialog, based on an extensive learning set. They will always find a plausible-sounding answer to a plausible-sounding question: so much learning material correlates to that.

Before epistemology is introduced explicitly into their architecture, language models will remain literary devices, so to say, unable to tell "truth" from "fiction". All they learn is basically "fiction", without a way to compare to any "facts", or the notion of "facts" or "logic".