I took (and failed) the test that was part of the study described in this article about perfect pitch being genetic. The tones that were generated were computer tones that were devoid of any kind of "color." Simple pitch recognition, or the ability to register the number of oscillations per second that a given pitch goes through, is what that study measured.
Like most musicians, I have relative pitch. I can also identify pitches when they are played on any of the instruments I have spent a lot of physical time with: violin, viola, flute, and recorder in particular, because I respond to those instruments by physical sensation, but that's not perfect pitch. Perfect pitch is absolute pitch. The kind of pitch that I have tried to develop. The kind of pitch that my brothers were born with.
The above article suggests that the ability to perceive pitch "goes sharp" when we get older. I don't think that a change in mental ability is the cause. I know of three older people who have complained that they hear pitches half a step sharp (one is my father--who only has the problem when listening to recordings, one is my friend's father, Louis Teicher, and one is Svatislov Richter). I imagine that there must be something physiological about the hearing mechanism that causes pitches to be heard sharper that comes with age. Only someone with perfect pitch would notice, though.