That's what is called "studying" or "reading a textbook", isn't it?

Did you just sit there in class and then never do anything with what you learned afterwards? That certainly isn't how I approached university.

The real answer is:

You should have a mental model about how the world works and the fundamental rules of the context where you're operating. Even though you might not know something, you eventually develop an intuition of what makes sense and what doesn't. And yes, that applies even to "university lectures" since a lot of professors make mistakes/are wrong plenty of times.

Taking an LLM's output at face value would be dumb, yes. But it would be equally dumb to take only what's written on a book at face value, or a YouTube video, or anyone you listen to. You have to dig in, you have to do the homework.

LLMs make it much easier for you to do this homework. Sure, they still make mistakes, but they get you 90% of the way in minutes(!) and almost for free.