I'm fascinated by this discussion because of how imprecise the terms "perfect," "absolute," "pseudo-absolute," etc. are. It's doubly interesting because we're describing things that happen in our own minds, with each of us having potentially different abilities and training and no common reference to what a "typical" person can do.

For me, sometimes, I can hear the opening note or chord of one song and it will immediately remind me of another unrelated song. When I check, they're almost always either in the same key or a semitone off. It happens most reliably when the timbres are similar. It's not a conscious thing, and the more I try to make it happen the less it ever does. Oddly enough though, I am terrible at identifying intervals. (Major third, perfect fifth, yeah, I know they're different and I can hear that, but ask me out of the blue which one was just played and I'll manage to get it wrong.)

Another thing I can do is play what is essentially a "mental recording" of a song I know well in my head. It's like if I had an iPod, and I felt some urge to listen to "La Grange" by ZZ Top, I can hear it in my head -- guitars, drums, vocals. I can skip around to whatever part interests me. I find that when I start tapping out the rhythms of what I'm recalling, or humming along with its melody, my recollection is pretty spot on when played against a real recording on speakers. Again maybe a semitone off at worst.

Both of those suggest to me that, somewhere in there, I do have an absolute pitch reference that I'm drawing from in an undisciplined way. If I sat down and practiced I bet I could refine it, but... why? Might be a neat party trick, but aside from that I don't really feel like I'm missing anything without it.