There is nothing hopeless or muddled about learning to recognize and produce pitch. Nor should there be a rule that says children are better at learning it unless someone has an effective teaching method and has used that method equally for both child and adult.
It is something that can be learned through training: not intellectual analysis, and not passively by listening. I got the beginning end of such training last year and whatever I have has stayed. The odd thing is that I cannot recognize pitch name with my mind (yet) - it goes by intermediary of an instrument. I can hear a tone, or sing a tone, and if I go to the piano or other instrument I play, my finger will accurately, each time, pick out the note, and then I will know which note it is after seeing what my finger picked. So there must be a pitch awareness associated to the instrument which is sitting in an area of consciousness (um, unconsciousness). It was definitely trained, though. I was taught by singing scales, which had to be accurate, and being aware of both pitch and relativity as sound and name, being aware of the tone I wanted to produce before producing it, and then making certain that was indeed the correct tone. It was a rather intense process.
It has a bit of a drawback on piano, because I was trained to adjust for the nuances that happen in a scale, where the leading note, for example, is sharpened, or to want a chord to harmonize within the notes. The piano has been tuned in a compromising way to incorporate all keys, in equal temperament tuning. I can hear that, and I want to reach in and adjust the strings becuase they sound "out of tune" even if it is a tuned piano.
Pianists don't have to produce pitches. In fact, they can't if they wanted to becuase the piano is pre-tuned. Is there any practical application to having this ability, other than to recongize that you are playing in the wrong key or to find your way to a modulation by ear (which is also and mainly relative, not absolute)?