Do I have perfect pitch??

So I have this party trick that I discovered a few months back:

You give me any song that I’m semi familiar with, I give you the pitch the song starts in (without hearing the song beforehand), you play the song on spotify (or wherever) and I get right it 99% of the time (the only time I don’t get it is when I haven’t heard the song in a loooong time or I confuse the original with a cover I’ve heard that’s in a different key).

Now, I can’t name the pitch as a note (B, A#, Db…) but I can sing the song in the correct pitch always. But I know, because I checked online, that f.x. David Bowie’s “Heroes” starts with a D. So if I need to find D, I just sing “Heroes” in my head and I got it.

I am also an actor, I do musical theater, I can barely read sheet music but I’ve never had any trouble learning harmonies, no matter how complex they are or how much my much more experienced cast members struggle.

It seems to me I just have really good pitch memory but I was wondering if I maybe do actually have perfect pitch but I just don’t know what A# (fx) “sounds like” and if I’d had music theory training when I was younger, I could name notes like you lot can?

Hope you can help me!