Every day I see people who do not seem to know LLMs use web search and cite sources.
Yes, AI Overview is a pretty weak model, but it somehow got "yes, that photo is AI" from an article explaining "not only is that photo not AI, here is the reporter who took the photo."
The other thing is that it is often hard to tell whether a model is talking about a source because the surrounding system has run a search and injected it into the prompt, or whether it's just freestyling based on its training data.
They absolutely cannot correctly cite sources otherwise.