I hate to get really pedantic here, but the concept of "truth claims" plays fast and loose with concepts of the knowledge in a philosophical sense. The idea of "fact checks" misunderstand how information and knowledge work together. Knowledge is about evidence, not "facts" because facts are a shorthand for a preponderance of evidence.

I feel we are doomed to debate the veracity of Wikipedia on a loop, forever, because people don't understand that Wikipedia exists as a place to find citations not as a place to find facts. Yes, those stated facts may disagree with the citations, but even if we try to fix that issue by having experts write the encyclopedia, we still suffer from the problem that the experts are often wrong.

We need a view of knowledge's relationship to LLMs that is based in Karl Popper's idea of falsifiablity. We should ask LLMs for evidence of claims not for truth values. Truth values are foundational to deductive systems, where axioms define truth. In inductive systems, like the real world, the concept of black swan events means that truth values are never fixed and are always in a state of uncertainty.

I honestly think it would be helpful going forward if we add some basic philosophical education to the standard curriculum, because no that we have an artificial form of information retrieval, we need to be much, much more pedantic about how we interpret that information.