I played in a band with a bass player who had no BS perfect pitch. It was pretty amazing. And the dude could listen to any song one time - maybe twice max - and have the entire piece committed to memory in his head so no FF/RW to pick up the details. He did that part in his head. Musical savant.
I definitely do NOT have perfect pitch, but I did work with one or 2 of those 'ear training' courses that you could order back in the day. It definitely helped me develop my 'relative' pitch as far as identifying chord voicings and intervals.