I mean, how do you live life?
The people you talk to in your life say factually wrong things all the time.
How do you deal with it?
With common sense, a decent bullshit detector, and a healthy level of skepticism.
LLM's aren't calculators. You're not supposed to rely on them to give perfect answers. That would be crazy.
And I don't need to verify "every single statement". I just need to verify whichever part I need to use for something else. I can run the code it produces to see if it works. I can look up the reference to see if it exists. I can Google the particular fact to see if it's real. It's really very little effort. And the verification is orders of magnitude easier and faster than coming up with the information in the first place. Which is what makes LLM's so incredibly helpful.