that indicates the LLM has a concept of truth vs. being good at linguistic pattern matching to return language that accurately classifies true and false statements
"It doesn't know the difference between true and false, it only knows the difference between true and false."
The second thing you mention "good at accurately classifying true and false statements" is literally knowing the difference between true and false.
Edit: You might also want to familiarize yourself with the first paragraph in 1.1 as you seem to be under a misconception at odds with research over the past year.