Assume that you go to a live concert. Further assume that you have hearing loss in the 600-800Hz region. Despite that loss, your brain tells you that what you're hearing sounds correct, natural.
Not necessarily. There are at least a few possibilities I can imagine. One, it is doubtful that this music concert is the only reference and even more doubtful that it can serve as a reference for accuracy unless a whole lot of things are accounted for including room interactions and frequency responses, distortion at the listener position, etc. So, it would still only serve as one data point and probably not an ideal data point in a sea of other data points.
If we play that recording in your room, which we'll assume has a flat response
How many rooms have a flat response?
you're still experiencing it in the context of your hearing loss and it still sounds natural to you.
How do you quantify the hearing loss? Were you born with it or did it degrade over time?
If we then EQ out your hearing loss by adding volume in the area of that loss, we're adding to the original event and, in theory, it should no longer sound natural.
It would not sound natural to someone who has perfect hearing, but how do we know it doesn't match some data point in the listener's head -- even if it is only an idea of what sounds right in his or her head? And how do we know that that idea is incorrect?
Another problem I can see with this theory is that increased bass or treble or other tone controls are what is being called into question here, correct? Why do some people with normal hearing experience deviations from flat as pleasurable? Why wouldn't a person with some hearing sensitivity or insensitivity experience a system and room that was tuned to compensate also find it pleasurable -- for the reason that it make the system sound more accurate according to an internal picture that may in fact be accurate and we have no way of knowing for sure?
Also, we never did deal with the idea that some amount of distortion may be necessary for suspension of disbelief.
And -- in your hypo above, what if some of the musicians were using tube gear, would the sound of tube distortion also become a reference for natural sound?