I think it very likely that the chief element in the make-up of a prodigy is listening, both to their own play, and to others'. Like exceptional athletes, they somehow "get" what matters quicker, and it's this that accelerates them more than greater "ability." (Or is that merely what all "ability is?)
I'm not conviced by the "magical thinking" argument. A teacher once told me she could feel me "counting like mad" during a long quiet chord. "Just listen to the chord," she said, "and it will tell you when to move on." I tried it, and, like magic, it worked. Of course I had acquired listening skills I was unaware of, and the decay of the chord was familiar to me from many hundreds of others, so that the moment to move was "rationally" arrived at. That rational process, though, was too intricate to articulate. I think much of music works like this. Think of the physical complexity of a "good" tone on a brass instrument (about which, of course, you know far mor than I). The mathematics of the sound waves in the air alone would require a good chunk of pencil work to be expressed, let alone the contact between lip and metal, vibration of the bell and so forth. It's actually remarkable that our minds, armed with a fairly simple listening device, can distinguish between various instruments so easily, let alone between good and bad tone. Have you read about the sonar operators who could identify copper in a ship's hull? I don't believe they have yet determined what in the tone-package allowed them to do this. That doesn't mean I think it's magic, the answer could be found if enough time is devoted to it. Think of how easily we can understand a Scot, or a Malawian , speaking English. Every word they say is very different from our version of the word but we are able to judge the distances between their vowels and consonants and recognize equivalent differentiation in our own. "Like" magic, but of course not magic. (I believe, and I have lived in places where most people believe in magic, that this is how "real" magic itself works, rather than the other way around, although I've encountered evidence against this thesis.) Processes may be inaccessible without being magical. Isn't this the "somehow" you italicize?
I recognize the holier-than-thou moral attatchment to slow practice lampooned above, but that's simply a human failing. That sort of self-centeredness can detract from music in a thousand ways- it is not exclusive to slow practice. I certainly can't imagine that it gives any impetus to Walter in making his argument.
On a lighter note ( and one I know a hell of a lot more about) real competitive tennis players respond instantly to their opponents' play (e.g. two identical serves). Weak players and weak competitors are caught up in their own problems (why am I not hitting the ball like I was yesterday) instead of focusing on what their opponent does, and how to take advantage of it. The problem with two identical serves with a 75% chance of success is that in tennis all points are not equal. In squash you count points up to 11, and when you have 11 you win- all points count the same. In tennis, because of deuce scoring, some points are crucial, and some matter not at all. If I'm serving at 40-0, I'm not too worried about the outcome of that point. On a crucial point, say 30-40 serving, it is wise to have a bigger serve with a lower chance of success, as long as you have a back-up with a 98% chance. I'm not even taking into account the myriad mental factors at work on both sides of the net, although the most obvious is that a player faced with identical serves will become extremely comfortable with the return. I could spin the ramifications out for pages, and never cover them all, but there are 17 year-olds who somehow grasp them and internalize them even though they can't express them. OOps, getting serious again.
Probably very self centered of me to write at such length. Cheers, Sasha