The point is not whether somebody has ever tried to associate neural nets with probability, sorry if my previous comment made it seem that way. The point is that neural nets are not fundamentally tied to it. You can try to tie them to probability, but you certainly don't have to, it mostly isn't, it isn't mostly taught that way, and the big open problems in the field don't involve it.

Statistics works the other way. You basically always start with some kind of probabilistic model. And then, if you even bother with prediction, you work towards prediction from the probabilistic model. With stats you don't need to interpret or add probability after the fact, it's already there.

Obviously stats and ML are enormous fields, with quite some overlap. And people tend to go after low hanging fruit; if many people who studied neural nets have formal probability backgrounds it simply makes sense that someone will write a paper on it. And I'm generalizing here (same goes with frequentist & Bayesian comment). But there absolutely is justification for saying "neural nets are not really a statistical technique".