The logical skills to evaluate the output of a LLM are the same skills brought to bear reading any book. What makes you trust this textbook then? Textbooks are not infallible.
But why not both?
That's an assumption increasingly false, unfortunately. The spirit of collegiality has been beaten back.
Far better to hone logical skills that sift between fact and error than to rely on social reputation. Ironically we're discussing a text designed to do exactly that.
The savvy LLM user already knows to be on the lookout for falsehood, if not bad pedagogy. That's a benefit, not a drawback of LLMs.