Having a confidence score isn't as useful as it seems unless you (the user) know a lot about the contents of the training set.
Think of traditional statistics. Suppose I said "80% of those sampled preferred apples to oranges, and my 95% confidence interval is within +/- 2% of that" but then I didn't tell you anything about how I collected the sample. Maybe I was talking to people at an apple pie festival? Who knows! Without more information on the sampling method, it's hard to make any kind of useful claim about a population.
This is why I remain so pessimistic about LLMs as a source of knowledge. Imagine you had a person who was raised from birth in a completely isolated lab environment and taught only how to read books, including the dictionary. They would know how all the words in those books relate to each other but know nothing of how that relates to the world. They could read the line "the killer drew his gun and aimed it at the victim" but what would they really know of it if they'd never seen a gun?
I think your last point raises the following question: how would you change your answer if you know they read all about guns and death and how one causes the other? What if they'd seen pictures of guns? And pictures of victims of guns annotated as such? What if they'd seen videos of people being shot by guns?
I mean I sort of understand what you're trying to say but in fact a great deal of knowledge we get about the world we live in, we get second hand.
There are plenty of people who've never held a gun, or had a gun aimed at them, and.. granted, you could argue they probably wouldn't read that line the same way as people who have, but that doesn't mean that the average Joe who's never been around a gun can't enjoy media that features guns.
Same thing about lots of things. For instance it's not hard for me to think of animals I've never seen with my own eyes. A koala for instance. But I've seen pictures. I assume they exist. I can tell you something about their diet. Does that mean I'm no better than an LLM when it comes to koala knowledge? Probably!