Or as trustworthy as any other human. Humans often believe things that are objectively not true and yet they will use these things to judge other things by.
Humans usually try not to lie, and there's a particular shape to the sorts of details they tend to forget / confuse. Compulsive liars often don't even notice themselves lying. That's closer to an LLM. I trust the output of an LLM about as much as stuff George Santos says.