That's a big problem if you're using a language model as a search engine. The trick is to learn how to use them for the things that they're good for outside of that.
^^ this. For instance, LLMs are really good at turning natural language into SQL. And if you know SQL, you can read it and make sure it looks good. But, it's much faster and easier than writing SQL by hand.
But that's still "You have to check any facts against expert sources"! You just have the advantage of being your own personal expert.
Verifying a solution is easier than coming up with it.