Interesting study, thanks for posting it, Jack.

Further to McGrath's point, and I think related to the variable perception of "correct", here's a link to a chart of historical pitch information at dolmetsch dot com. The numbers in the leftmost column are for A above middle C, which nowadays is 440 Hz in a majority of Western music (maybe other music too, I wouldn't know). It shows how pitch norms have changed with time and place, making it clear that "perfect pitch" has nothing to do with an absolute value.

Like Highlandman I have great relative pitch, and my ear is fully flexible to include tunings that lie between the standard notes (as when a guitar is tuned slightly sharp or flat but not all the way to the next semitone). I find that this sense of relative pitch can also be both gift and curse.

When I hear music that's out of tune within itself, I can't help but edit as I listen; in effect I automatically "transpose" the wrong notes to correct ones. Compère two reeding uh cent ents fulluv rong speh Ling, ore wurce, uh hoal stoarie. I can no more listen without correcting than I can read the previous sentence without visualizing the correct spellings or audiating the correct words. The further out of tune a note and the more complex its underlying harmony, the greater the number of workable options to sort through on the fly, which makes listening to out-of-tune jazz more laborious than out-of-tune bluegrass. It takes at least an equivalent effort to force myself not to re-process the intervals in my mind's ear, maybe even more effort. To ignore tuning errors is easier though when I'm singing or playing along, whether harmonizing with an out-of-tune melody or singing with an out-of-tune guitar or banjo. Anyhow, all that is to say: My way to understand folks with perfect pitch who are bothered by transposed music is to think of them imagining each note and chord in its original key as the piece or song unfolds.