For what it's worth, I have the exact same skill as you down to all of the details. I can remember many songs in their original key, sing them / whistle them within a few cents usually, identify the key of many notes most of the time, but by no means 100% of the time perfectly. It's probably something that could indeed be trained to be more "perfect", but as someone who does have "pretty good" absolute pitch, I still consider it a parlor trick. It's fun now and again, but it doesn't really help much with my music. Perhaps that's because I don't transcribe Bach concertos.
On the other hand, I completely agree that relative pitch has to be on point. I don't see how it's possible to be an effective musician without it. Being able to intuitively know intervals, certainly if you're a singer, is indispensable.
On the other hand, I completely agree that relative pitch has to be on point. I don't see how it's possible to be an effective musician without it. Being able to intuitively know intervals, certainly if you're a singer, is indispensable.