Could you expand on that? It has never been clear to me what music theory is — what constitutes true or false claims about the structure of a piece of music, and what constitutes evidence bearing on such claims.

You're in good company, because it's never been clear to music theorists either, even after a couple millennia of thinking about the problem.

However, I do have my own view on the matter. I consider the music-theoretical analogue of "matching the territory" to be something like data compression. That is, the goodness of a musical theory is measured by how easily it allows one to store (and thus potentially manipulate) musical data in one's mind.

Ideally, what you want is some set of concepts such that, when you have them in your mind, you can hear a piece of music and, instead of thinking "Wow! I have no idea how to do that -- it must be magic!", you think "Oh, how nice -- a zingoban together with a flurve and two Type-3 splidgets" , and -- most importantly -- are then able to reproduce something comparable yourself.