There is a fun experiment you can do yourself to show that you have the capability for Absolute Pitch. Think of some pop songs or specific music recordings that you like listening to. Sing it, or play it in your mind. Then listen to the actual recording. If you can do this with some songs, then you have (at least the capability for) absolute pitch.
The reasoning is simple. You can sing a song in any key you like (within the bounds of your vocal range). You don't even have to sing in a standard key. (You could sing it half-way between C# and D for instance). If you pick the exact right key out of the effectively infinite possibilities, you have remembered a specific pitch. If you can remember specific pitches, you can label them. (It's just that music always makes things easier. Writing a song to memorize something is an underused technique IMHO).
I can do this reliably for songs I've listened to recently (within the last couple of days), but after that I somehow "forget" the pitch. If I played a C scale on my guitar a few times in the morning every day, I could probably identify pitches correctly based on that reference. But I'd still need the reference.
The reasoning is simple. You can sing a song in any key you like (within the bounds of your vocal range). You don't even have to sing in a standard key. (You could sing it half-way between C# and D for instance). If you pick the exact right key out of the effectively infinite possibilities, you have remembered a specific pitch. If you can remember specific pitches, you can label them. (It's just that music always makes things easier. Writing a song to memorize something is an underused technique IMHO).