I understand your point, but who knows if these things aren't really the same? My opinion is that having the notes "burned" in your memory is a lesser degree of the same phenomenon. People that are considered to have "real" perfect pitch just developed these abilities beyond what normal musicians like you did. And doing this at a very young age really helps a lot, in the same way that leaning new languages in infancy is a painless activity and quite difficult at adult age.
Yeah - I guess the early acquisition might be what influences the way these kids develop different cognitive strategies for music early on. It's obvious when teaching kids: the median student seems to operate on the first order derivative of the pitch curve, while the perfect pitch kids operate with the absolute values. A gross simplification. Interestingly, many of them require a different strategy for transposing melodies: go note by note, while median learners apply melodic intervals incrementally. Similar differences can be seen in solfege and dictation.
