The axion may not be an example of the following, but there are highly specific predictions of new particles (etc) that drop out of current theory and knowledge. Antiparticles, from Dirac is one example. If they hadn't been found there would have been no motivation to look for something much like an antiparticle, since those variants wouldn't have fit into Dirac's theory.

So not speciously true of all predictions or most (before String Theory came along!)

You both may be correct. Fundamentally though the philosophy of science prefers a hypothesis that is falsifiable to one too vague to falsify.