My theory and composition teacher in college went through this same thing 100 years ago. I noticed she had a perfect pitch and asked her why. She told an identical story: that, at the kindergarten level, her entire class was taught how to recognize pitches. She was not impressed by her own ability, however, because her sister could identify the pitch of anything IRL, whether you kicked a rock, or you were listening to an exhaust pipe.
I also had a classmate who could identify any pitch to the exact frequency, so A443 versus A440, for example. Of course we tested him.
In the old days of PCs (maybe even now) there was a way to click the speaker at a specific frequency- I wrote a simple x86 code to click, delay, click, delay and proudly told my office mate that I could make my computer play A440.
He listened for a bit and said, nope that's 441 or so. I checked, and my program had a tiny bug where it wasn't delaying long enough. Fixed that, he verified it was now A440. He said he had perfect pitch and it was really annoying because almost everything was out of tune.
Did you ever test his ability to recognize pure sine waves?
Ofc, each note is actually composed of ~40 frequencies at different levels (timbre). That’s why different instruments playing the same “frequency” sound different
Heard somewhere that absolute pitch folks sometimes struggle with sine waves (no timbre)
I also had a classmate who could identify any pitch to the exact frequency, so A443 versus A440, for example. Of course we tested him.