I am surprised about the 1 in 10,000 number, but I can attest to what he is saying. I grew up hearing music even while in the womb. My mom was a musician. And I wound up having perfect pitch.
I can describe what it's like, but I honestly feel anyone can learn it with enough practice. (Never put it to the test though.) It's simply like reinforcement learning of being able to hit a note in a certain position. When you hit it too high or too low, you correct yourself, until you have a memory of where you are supposed to hit it properly. With children I am sure a lot of the "tuning" happens over multiple repetitions due to being exposed to the combination of "fa", "sol" or "the start of star wars" always referring to the same thing.
I think you could teach your kids the perfect pitch by having them sing songs with "do re mi" terminology (or possibly ABC-G but that's a bit worse because it's not a natural major scale) and having them do it over time adjusts their brain's "predictions" of where they should hit the note. If they deal with music all the time they'll be able to do it. It's similar to picking the right vocal tone for a situation or a basketball player knowing how to shoot a ball after many tries. A tennis player hitting a ball is a bit harder because the action must be a function of the input.
Now, as I got older, switched careers and have been away from singing / playing music for a few years, I can report that my perfect pitch is still there but "modulated down" almost a half-step. So when I want to sing "do re mi" or a theme that I know is with D minor, I sometimes do it a half step lower. When I listen to that piece, it sounds a half step higher. (I am 34.) However, a few seconds of reinforcement learning that "no, this is D minor" and suddenly everything snaps back and I have perfect pitch again.
I believe that reinforcement learning across perfectly tuned instruments and songs all around is is what causes perfect pitch. So I always thought that, with enough exposure to music and having to sing the songs using do re mi instead of the words etc. anyone can form those associations and "tune them". Well, anyone who isn't lacking the brain capacity for tuning their pitch or actions or whatever. I would say that's more than 1 in 10,000 people. It just needs similar skills to motor coordination.