Yes... yes, it really does exist.
Somehow, I have a hard time believing that Tchaikovsky didn't have perfect pitch, but whatever.
I suppose you are right. They way I always saw it is that since both the number of composer and the number of people with perfect pitch is so small (at least compared with the rest of the world population), I assumed that a lot of those composers would have it. I guess I thought that there are more people with perfect pitch than there are composers, but you seem to say that it's the other way around! Or, at least, it's more complicated than that.
Personally, when I hear a piece that's performed in A=432 hz, I can still tell what key it's in, and can identify all the notes. However, when I hear a piece that's in "Baroque tuning" (really, just tuning it down a half-step), I have to understand that the piece has been tuned that way already, in order to identify the key. Also, there are times when I listen to an old recording of a piece, especially from a old film, and unless I actually have the original score for the music, I can only guess they key based on the A=440 or 432 method (though often times, it turns out that the recording is a half-step higher 🤔).
Take this recording, for example:
Since it's a score video, you have the notes in front of you, and thus you would assume that the audio would match the notes in frequency. But here, this is not the case: the recording (for some reason) is actually tuned a half-step LOWER. Thus, if you didn't have perfect pitch (to 440 or 432 hz), you would have no way of knowing that the tuning is off.