Take the Pythagoras example then. How is it different from parroting if you never even read and understood the proof? And alright, parroting might be a negative

Take the Pythagoras example then. How is it different from parroting if you never even read and understood the proof? And alright, parroting might be a negative word and you could want to use a fancy word saying you're following heuristics instead. But it doesn't change that you maintain and propagate knowledge that you have not personally verified in a rigorous sense. There are examples of things written in school books that were just plain wrong because no one bothered to properly verify it. We all settle for "good enough" most of the time.