[Bud]

It's not "cheating", but it's also not absolute pitch, by definition.

Absolute pitch (or perfect pitch) is the ability to identify a note without having any memory aid or reference tone to compare it to.

So if you have a constantly-present reference tone, due to tinnitus, and you figure everything out based on the interval from that tone, that's simple relative pitch and the ability to figure out intervals. Not perfect pitch.