I think that, where people have argued the veracity of perfect pitch, I would agree - to a point.
I could tell you precisely what note you were playing, at any given time - by working from F major. I would not, however, have the exact note out of thin air. It would require some (practised) math.
Maybe we're all tuned to a certain frequency, and when developed and honed, we can use that to our advantage?
All of my compositions begin in F Major - Unless I make a concerted effort otherwise!