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Pitch Perception Skewed By Modern Tuning
The feed deliverers us news of research suggesting that the use of A as the universal tuning frequency has made our ears less discerning of the notes immediately around it. Here's the abstract from PNAS describing research with people possessing the rare quality of "absolute pitch."
Adding to the shrug factor, the twelve-tone pitch system as a whole is a human invention. This makes perfect pitch that much stranger, because it means people have an innate ability to attune themselves to an artificial note naming scheme.
So since that scheme can vary somewhat, it would make sense that depending on "which" A your perfect pitch is tuned to, you may have trouble distinguishing G# or A# in a different tuning.
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No, no, no! Twelve-tone pitch is derrived from perfect intervals, such as perfect thirds, fourths and fifths. These can be defined very cleanly as the integer ratio between two frequencies (look up just intonation). The ratios are mathematically beautiful and simple, and also sound particularly good. The temperated (12 note) scale used by nearly all instruments today is an attempt to fit these intervals into a common scale. You may say that this approximation is a human invention (even though it's cleanly defined as freq = 440hz * 2^(n / 12), where n is the semi-note distance from A4), but as a whole? No.
In other words, it proabbly wouldn't make any sense to use a 16 note scale or something like that. The 12 note scale has roots in something very mathematical, not something random or "human".