Right, but now you are not talking about an LLM generating from it's training data - you are talking about an agent that is doing web search, and hopefully not messing it up when it summarizes it.
The net result is that some responses are going to be more reliable (or at least coherently derived from a single search source) than others, but at least to the casual user, maybe to most users, it's never quite clear what the "AI" is doing, and it's right enough, often enough, that they tend to trust it, even though that trust is only justified some of the time.