That's a different exercise though... wrong direction. Absolute pitch recognition is hearing -> pitch. What you describe is memory -> performance -> comparison <- hearing.
> Absolute pitch (AP), often called perfect pitch, is the ability to identify or re-create a given musical note without the benefit of a reference tone. [Wikipedia]
This is what I'm describing: knowing a song well enough that you can 'hear' it in your head, and use that to accurately identify and re-create a note from it. This is a few more steps than being able to simply 'know' a note upon hearing it but nonetheless can demonstrate the capacity to do so for those who haven't specifically practiced it.