the same knob that makes them unpredictable makes them invent “facts”.
This isn't what makes them invent facts, or at least not the only (or main?) reason. Fake references, for example, arise because it encounters references in text, so it knows what they look like and where they should be used. It just doesn't know what one is or that it's supposed to match up to something real which says what the text implies that it says.