At every point, during a knowledge/data search for reaching a particular goal, the onus is _always_ on the person searching to do their best to ensure that the sources they use are accurate, and they do the effort required to ensure that they translate that properly to fit that goal.

The education system I grew up in was not perfect. Teachers were not experts in their field, but would state factual inaccuracies - as you say LLMs do - with authority. Libraries didn't have good books; the ones they had were too old, or too propaganda-driven, or too basic. The students were not too interested in learning, so they rote-learned, copied answers off each other and focussed on results than the learning process. If I had today's LLMs then, I'd have been a lot better off, and would've been able to learn a lot more (assuming that I went through the effort to go through all the sources the LLM cited).

The older you grow, you know that there is no arbiter of T-Truth; you can make someone/something that for yourself, but times change, "actual, factual history" could get proven incorrect, and you will need to update your knowledge stores and beliefs along with it, all the while being ready to be proved incorrect again. This has always been the case, and will continue to be, even with LLMs.