> After paticipating in social media since the beginning I think this problem is not limited to LLMs.

Yup, but for LLMs the problem is worse... many more people trust LLMs and their output much more than they trust Infowars. And with basic media literacy education, you can fix people trusting bad sources... but you fundamentally can't fix an LLM, it cannot use preexisting knowledge (e.g. "Infowars = untrustworthy") or cues (domain recently registered, no imprint, bad English) on its own, neither during training nor during inference.