They don’t care about factuality, and in fact have no ability to “know” if they are correct. And they don’t “care”
I suspect that most people think (maybe not even consciously) that these models answer questions by retrieving data and then writing a response which incorporates that data, rather than just generating text that may or may not contain actual facts.
It really bears repeating over and over that all these so-called AI systems do is take a prompt and output text in response to it that reads as if a human wrote it.
I’ve told my wife that she doesn’t have to spend time with me if I end up with dementia and I start behaving that way. Both of my parents were more or less all there well into their 90s, but you never know.