I generally agree with you. But it is useful to have a term for training methods that use clever tricks to bypass manual data labeling, usually with some secondary objective in mind (that the model should do something that is not strictly the same as the SSL objective). In that sense, I think of it as a subset of supervised learning. In ML, literally every innovation gets its own catchy name. This is in contrast to, say, statistics, where major innovations often aren't named until years later. I suspect this has to do with the hotness and competitiveness of ML - you need a catchy name to stand out in a crowd of thousands of papers doing very similar things.