People in particular have evolved complex self protective mechanisms to provide the right answers for their given environment for safety reasons, based on a number of different individual strategies. For example, the overly honest, the self depreciating, the questioner, the prosecutor, the victim, the liar, the absent minded professor, the idiot, etc.
LLMs are not that complex or self-referential.
Personally, my guess is that you'd want to build a model (of some kind!) whose sole job is determining the credibility of given string of tokens (similar to what someone else noted in a sibling comment about high answer volatility based on minor input changes - that does sound like a signal of low credibility), and somehow integrate THAT self-referential feedback into the process.
Notably, even the smartest lawyers (or perhaps, especially the smartest lawyers) will have assistants do research once they've set out a strategy so they are sure THEY aren't bullshitting. Same with professors, professional researchers, engineers, etc.
Because until someone goes and actually reads the case law from a credible source, or checks the primary research, or calculates things, it's possible someone was misremembering or just wrong.
Being right more often is not about never having a wrong thought/idea/statement, it's about double checking when you're thinking you might be bullshitting, and NOT saying the bullshit answer until you've checked. Which is proportionally, very expensive. The really good professionals will generate MANY lines of such inquiry in parallel for folks to track down, and then based on their degree of confidence in each one and the expected context the answer will be used in, will formulate the 'most correct' response, which is proportionally even more expensive.
So at least during the process, there would be a signal that the system was likely 'bullshitting'. Which might help it in at least being able to signal when it's answers are low-confidence. (human equivalent of stuttering, looking down and away, looking ashamed haha!)
Every human gets fooled sometimes in at least some venue though.
That's certainly one root of the problem, but I would argue that there are multiple roots to this problem!
Humans have further realized that understanding itself is provisional and incomplete, which is quite a remarkable insight (understanding if you will), itself.
I don't know that that is quite the right question to ask.
Understanding exists on a spectrum. Even humans don't necessarily understand everything they say or claim (incl. what they say of LLMs!), and then there are things a particular human would simply say "I don't understand".
But when you ask a human "can you understand things?" you will get an unequivocal Yes!
Ask that same question of an LLM and what does it say? I don't think any of them currently respond with a simple or even qualified "Yes". Now, some might claim that one day an LLM will cross that threshold and say "Yes!" but we can safely leave that off to the side for a future debate if it ever happens.
General note: it is worth separating out things like "understanding", "knowledge", "intelligence", "common sense", "wisdom", "critical thinking", etc. While they might all be related in some ways and even overlap, it does not follow that if you show high performance in one that you automatically excel in each of the other. I know many people who anyone would say are highly intelligent but lack common sense, etc.