With enough training and practice, I do believe that most people can accomplish quite a lot. Will that trained person be as good as a naturally gifted person? It depends on if the "gifted" person "wastes" their ability or is also training as well. If someone can hear a 440Hz tone, and state that it is an A, then that's pretty damn good and in 99.9999% of the time good enough. If they hear a 439Hz tone and also call that an A, then that's pretty damn good as well. For the rare person that could say that it's 1Hz off, then sure, that's even better, but there's always someone out there better. The person that wins the silver metal at the Olympics but lost by 0.01 seconds is still a really damn good athlete.
So I'm not arguing someone can train themselves to be perfect pitch, but in all practical purposes it's close enough. If you can pin point the specific player in a group that is off pitch, it is still impressive. Does the person that can detect the 1Hz difference bring any more benefit than the person that says 439Hz and 440Hz is the same note? If it does and you're depending on a human for that level of accuracy, I'd suggest you're barking up the wrong tree and should be using intstrumentation for that.
So I'm not arguing someone can train themselves to be perfect pitch, but in all practical purposes it's close enough. If you can pin point the specific player in a group that is off pitch, it is still impressive. Does the person that can detect the 1Hz difference bring any more benefit than the person that says 439Hz and 440Hz is the same note? If it does and you're depending on a human for that level of accuracy, I'd suggest you're barking up the wrong tree and should be using intstrumentation for that.