Thanks, that’s interesting. I’ve been trying to whistle a middle C on and off since I watched those videos, and I was only a semitone off on the last two attempts. I don’t have a sensation of being correct with it, and it feel like it’s just a guess, but I will keep trying. 
I don’t have perfect pitch, but my brain tends to automatically repeat music, which causes me to remember it even unconsciously. I can sometimes whistle the music that was playing in a store 30 minutes earlier, even if I wasn’t paying attention to it and have never heard it before — but it’s usually only a verse and a chorus that I can recall, not the entire song, and the exact notes and phrasing might be modified slightly. The tendency is so strong that if I don’t feed my ears music, my brain will start to repeat a corrupted version of my phone’s booting noise or my alarm clock. 