> Think of a song you know best, one you've listened to hundreds of times: can you sing it or hear it in your head pretty accurately (edit - not accurate intervals, but accurate pitch)? If so, congrats, you have the capacity for perfect pitch.
Absolute pitch can't be self-assessed subjectively like this. Hearing a song in your head is meaningless because you don't have an absolute reference to compare to.
Also, please read the first line of the abstract: Absolute pitch in this context also specifically refers to identification of heard tones, not ability to produce those tones yourself (in your head or otherwise). The test for absolute pitch involves playing different pitches spanning an octave and measuring how accurately and quickly the candidate can identify each pitch.
The first line of the abstract:
> Absolute pitch (AP) refers to the ability to identify the pitch of a tone without external references.
Even studies of students at prominent music Conservatories have shown low prevalence among their students. These are people who have been training for years and started at a young age. So you can't expect to come anywhere near perfect pitch as a casual person singing a song in your head.
Absolute pitch isn't a strictly defined trait. The participants in this study improved their pitch identification abilities after intense training, but they still haven't approached the thresholds of absolute pitch identification used in many of the studies of music students.
A common theme among absolute pitch studies is that people who started music at a young age (typically less than 5) score higher on absolute pitch tests. This study doesn't undermine that fact.