The fight is about the predictor language in some cases. Because it's only a trivial difference to those who don't understand the details of how these things are made. In pre-training the model really is trained to predict the next token. What is being emitted by the model is, by structure, by training and by optimization, a prediction of the very next token.
What is emitted by a model during RLHF and RLVR is not, by structure, training or optimization, a prediction of the next token.
Right. But that's never what the discussion is about. This is the first time I've seen someone say, "it's not just a next-token predictor because a bunch of the training isn't about predicting the next token." I have seen many, many people say "it's not just a next-token predictor because there's all this smart stuff going on inside the model." Even here, in the comments for an article that's all about the former, most of the objections to "next-token predictor" are of the latter form.