Yes this is correct. The thing is not about the term next-token predictor being correct, but because of the connotative weight of that phrase as a implicit trivialization of LLM abilities, which is how it is often used.
From another point of view, campaigning against the "next token predictor model" is a means to implicitly inflate LLMs' abilities. Given all the other hype-inducing terminology we've seen--"reasoning", most egregiously IMO--this seems more likely. Is there a simple, more accurate mental model? From what I've seen of the literature, "next token predictor" is a very accurate first order description of what an LLM does, I can't really do better, therefore this or that connotative interpretation isn't giving me a great deal of pause.
What is the motivation behind advocating against people trivializing LLMs? As in, why do you care?