I think that perfect pitch allows is a mental fluidity such as we all have with words.
It’s probably as easy for them to memorize the notes as it can be for us to memorize sentences.
Because my mind has such an intuitive grasp of English, it’s very easy to memorize and repeat what someone just said. They probably feel same about repeating and remembering music phrases as we do reapeating what someone just said to us.
Lucky mother f’s lol
This is absolutely not true. Rick Beato is one of the most brilliant improvisers, teachers, theorists, etc and he says (in the same video posted above I believe) that he does not have perfect pitch, although his son does. I would say that the majority of musicians, even the greats, do not have perfect pitch. It’s important to define perfect pitch. Perfect pitch is the ability to hear ANY pitch and properly identify it with no previous reference - whether it’s a frog or a car horn or a tuba. I have heard that non musicians can have perfect pitch and not even be aware. Relative pitch is the ability to identify a pitch from a previous reference.
Entertaining example: I know from my handy piano app that my electric tooth brush hums a B lol. I was brushing my teeth and heard a song on the TV in the other room that I had never heard and I could tell from my well developed and constantly practiced sense of relative pitch that my tooth brush was humming a minor 3rd relative to the song. So I knew the song must be in Ab.
In my opinion, the latter can be worked to a very high level. I can hear almost any song and immediately figure out the chords and melody. And there are countless times where I am playing a song on stage at a gig that I have never heard before. But, I have also worked on learning songs by ear from day one. I never learn a song, riff, chord or solo by tab or sheet music. I was also lucky enough to have a great ear training course in college.
Perfect pitch? I’m not sure if it’s achievable as an adult. More importantly, I don’t believe it’s necessary apart from bragging rights. I have gotten through my professional life as a musician just fine with out needing the ability to tell what note the 18 wheeler that just passed by was humming.
I would venture to say that most elites have a very developed sense of relative pitch.
Also, I think there is a large scale misunderstanding with musicians or the musically inclined to associate perfect pitch with talent. Like it’s the be all end all. I know people who claim to have perfect pitch and they are by no means on a world class, elite level of musicianship.
My several cents on the topic 
Edit: just thought of an elite level reference. There is a world class jazz player where I’m from. I was lucky enough to be able to take lessons from his teacher. His teacher told me that this guy has perfect pitch and has the ability to play any note that is in his head. I have listened to this guy extensively for over a decade on recordings and I do not hear evidence that he can pull new notes out of his head. Because there is a lot of repetition in his improvisations from song to song (mind you this doesn’t stop him from being one of the best jazz guitarists on the planet). But it sounds more like worked out formulas than this esoteric, untouchable realm of being able to pull notes from the depth of the soul, as his teacher would suggest.
Also, I believe that you lose it as you get older too…
I wouldn’t know how to quantify that. I can say that my sense of relative pitch just keeps getting better in my 30s - I can identify notes and keys sometimes just from hearing them now. Whereas a few years ago, I couldn’t. But that may change when I’m 70.
I think its a known thing that happens - the perfect pitch drifts off. Relative pitch however is retained (as far as I know), probably because you can train relative pitch…
This is exactly how she says elite people play, they hear the exact instrument in their head, as if it is off a tape, and their fingers make the sound in the real world.
Perfect pitch is not a skill. It’s inherent. Relative pitch is earned and invaluable. Very easy to understand. Although having an ear for music is also very important. And that is also an inherent skill but one that can be added to.
That’s kinda my point though by mentioning that. The guy I’m talking about is one of the best jazz guitarists out there. Very well respected. But from what I hear on his recordings and numerous live concerts, I’m not convinced he has this inhuman ability to extract notes from his soul - I just think he worked his ass off. Like Steve Vai. Steve Vai claims he isn’t naturally talented. He said in an interview that he can’t play even a very simple song on piano. I would think if he had this esoteric ability to summon notes from the center of the universe, he could play any instrument just as well as guitar.
Classical music is generally read from a page, referenced with recordings, memorized and then turned into the performer’s own interpretation. That’s where the spirit is. I’m not buying that every pro is summoning notes from some lofty realm that we can’t reach. Unless we are talking about freaks like Jacob Collier, who does, in fact, play any instrument on a virtuoso level. With someone like Jacob Collier though, it’s more than just perfect pitch. There is genuinely something turned on in his brain that other humans don’t have access to. I would not say this if he was a single instrument virtuoso like Steve Vai. But not only does Jacob have perfect pitch, he also has an extremely advanced knowledge of theory, harmony, technical ability and rhythm.
I would think if someone had the ability you speak of, they could summon new notes, patterns, ideas, etc on the fly. You could say jazz improvisers do this. But do they REALLY do it? I know a LOT of theory. And a LOT of harmony and scales. I can improvise pretty well over all but the hairiest jazz or fusion progressions. And if I have time to work it out, I can play over that too. Coltrane had the ideas for Giant Steps (one of the scariest chord progressions on the planet) worked out for a LONG time before he recorded the album. Listen to Tommy Flanagan’s piano solo on Giant Steps. That’s the sound of a world class, elite pianist basically sight reading that tune. And it sounds NOTHING like Coltrane’s fire. I would think if he had the ability your girlfriend speaks of, he would have sounded like Coltrane. Or better.
I’d like to say btw I hope that doesn’t come across the interwebs as ornery. 
I don’t mean to discredit your girlfriend. My main point is I don’t think this stuff is magic. When I watch a brilliant performer, whether it’s John Petrucci or Diana Krall, I think what I’m seeing is the result of hard work and maybe even obsession. And, as far as I know, neither Petrucci or Krall have perfect pitch. Petrucci in a recent interview talks about the difficulties of remembering how to play back catalog Dream Theater songs. So it’s obvious that he cannot simply envision the music and then play it. So if it takes rote memorization for someone on the level of Petrucci, I’d say it’s de facto for pretty much anyone else.