I think I know what you're after (notice my self-awareness to qualify what I say I know): that the tool's output can be relied upon without applying layers of human judgement (critical thinking, logical reasoning, common sense, skepticism, expert knowledge, wisdom, etc.)
There are a number of boulders in that path of clarity. One of the most obvious boulders is that for an LLM the inputs and patterns that act on the input are themselves not guaranteed to be infallible. Not only in practive, but also in principle: the human mind (notice this expression doesn't refer to a thing you can point to) has come to understand that understanding is provisional, incomplete, a process.
So while I agree with you that we can and should improve the accuracy of the output of these tools given assumptions we make about the tools humans use to prove facts about the world, you will always want to apply judgment, skepticism, critical thinking, logical evaluation, intuition, etc. depending on the risk/reward tradeoff of the topic you're relying on the LLM for.
It's not a fundamental fix, it doesn't even change the model itself, but the output might be more useful. And then there was just some speculation how you could try to train a new AI mimicking the more useful output. I'm sure smarter people than me can come up with way smarter approaches. But it wouldn't have to do with understanding - when I said the tool should return 'I don't know' above, I literally meant it should return that string (maybe augmented a bit by some pre-defined prompt), like a meaningless symbol, not any result of anything resembling introspection.
From a certain perspective, there does appear to be a rational mystical dualism at work.
When humans say "I know" it is often not narrowly based on "book knowledge or what I've heard from other people".
Humans are able to say "I know" or "I don't know" using a range of tools like self-awareness, knowledge of a subject, experience, common sense, speculation, wisdom, etc.