I think what it is, is that it's murky whether perfect pitch is the ability to name notes, or the capacity to learn to be able to. Historical thinking has mostly been that the two are the same, however I'm referring to it more as the former whereas you're referring to it more like the latter.

So I guess the point I'm trying to make is that the two aren't the same, which is more or less what's being supported by the paper. People might have the capacity to learn the ability (as the 'listen to a song in your head' exercise I described aims to demonstrate) and think they don't, because the common perception is that if you don't have the ability you don't have the capacity to learn it. Or something like that.