You're just arguing about semantics. It doesn't matter in any substantial way. Ultimately, we need a word to distinguish factual output from confidently asserted erroneous output. We use the word "hallucinate". If we used a different word, it wouldn't make any difference -- the observable difference remains the same. "Hallucinate" is the word that has emerged, and it is now by overwhelming consensus the correct word.
> Whenever they get something "right," it's literally by accident.
This is obviously false. A great deal of training goes into making sure they usually get things right. If an infinite number of monkeys on typewriters get something right, that's by accident. Not LLM's.