Have you interacted with AI in the past two years?

Of course LLMs are capable of generating factual information. An LLM wouldn't lie if you asked "is the earth round?". But an LLM won't generate factual information every time, because as much as the technology is getting hyped up, it's still quite limited and probably will be for the foreseeable future.

But when the answer is obvious and well-known, they are good enough. Just pop OP's question into any chatbot. They all, including Google's AI overview, give "no" here.

A state-of-the-art glorified autocorrect will not send "Absolutely!" as the first few tokens after "can cockroaches live in your penis". That's GPT-2 level stuff.

I agree with your last point about Google Search's decline.