I'm no expert, so take what I'm about to say with a grain of salt.
Fundamentally, a LLM is just a fancy autocomplete; there's no source of knowledge it's tapping into, it's just guessing words (though it is quite good at it). Correspondingly, even if it did have a pool of knowledge, even that can't be perfect, because the truth is never quite so black and white in many areas.
In other words, hard.
If you ask the FSF, open source is a bigger set than free software, mostly to do with restrictions on the uses of the code
https://www.gnu.org/philosophy/categories.html.en