[thaumasiotes]

Sure it's fair. Bitwise operations produce pretty strange numeric results, so no, I wouldn't think you'd expect much going in. But I don't see where the identity function comes into it at all. It looks like the term "the identity function" stuck in your mind, and you reached for it when you found something subjectively similar. But shared semantic space isn't a good reason to say that a function which isn't the identity function, is. Your middle point is the observation "f(a,a) = a", which is perfectly valid, but is not the same finding as the finding you report. Using pretty-simple terms to state something true is generally preferable to using even simpler terms to state something false.