When a kid at school is being taught, say, Newton's laws of motion, or what happened in 476 CE, they're not experiencing the empirical truth about either. They're only learning the consensus truth, i.e. the correct answer to give to the teacher, so they get good grade instead of bad grade, and so their parents praise them instead of punishing them, etc.
This covers pretty much everything any human ever learns. Few are in position to learn any particular things experimentally. Few are in position to verify most of what they've learned experimentally afterwards.
We live in a "consensus reality", but that works out fine, because establishing consensus is hard, and one of the strongest consensus-forcing forces that exist is "close enough to actual reality".
If we look at Newtonian mechanics, then various independently verifiable experiments are examples of Correspondence truth, and the minimal mathematical framework that describes them is an example of Coherence truth.
Fine, but it's not how any of us learned of it either - whether the Newtonian mechanics or the "4 theories of truth".
I mean, coherence is sure a an important aspect of truth, and just by paying attention whether it all "adds up" you can easily filter 90% of the bullshit you hear people (or LLMs for that matter) saying - but even there, I'm not a physicist, I don't do much experiments in a lab, so when I evaluate if some information is coherent with Newton's laws of motion, I'm actually evaluating some description of a situation against a description of Newton's laws. It's all done in "consensus space" and, if an answer is expected, the answer is also a "consensus space" one.
We're all so used to evaluating inputs and outputs through the lens of "is this something I expect others believe, and others expect me to believe", that we're almost always just mentally folding the indirection through "consensus reality" and feel like we're just checking "is this true". It works out okay, and it can't really be any other way - but we need to remember this is what we're doing.
There are multiple kinds of truths.
'Statistical truth' is at best 'consensus truth', and that's only when LLM doesn't hallucinate.