LLMs are as trustworthy as humans.
Humans have been being wrong for about as long as we have been lying.
Whether you get information from a human or an LLM, check it.
I worry about the people who insist on credible sources rather than checking information for themselves. I think 80% or more of them are trolling me, but there are some who genuinely do not apply the Scientific Method to check facts in their everyday life. I truly feel sorry for them.