Some more thoughts on the technician versus musician struggle and the technical replication of music…
In the more classical realm of music one of the main things that get pushed by good teachers is using etudes or studies books. This is very well known among orchestral players, pretty well known amongst horn players, maybe a little known by your average guitarist-at-large type players, and unknown by most of the listening public. These books contain a bunch of different pieces, maybe 2 to 3 pages long at most, in all sorts of different keys, crazy fingerings, and patterns and jumps that are tough for your instrument. For example with my instrument, the saxophone, books like “Enseignement du Saxophone” by Marcel Mule and “48 Famous Studies for Oboe or Saxophone” by Ferling. And every other instrument (trumpet, violin, etc) has their own set of specific study books. So, the point of these books is to learn these studies… and I mean really learn them. The first step is to just be able to read and play them, the second step is to have all of them memorized and memorized to the point where you don’t even think of the notes any more, and the third step is where the real studying begins. You are supposed to take the studies and play them fast, play them slow, play them legato, play them staccato, transpose them into different keys…. really learn the nuances of your instrument. Now, back when I was playing a lot I could rip through those studies incredibly fast just because I was so familiar with them. It would blow the socks off of people that had never heard them before due to the speed and range of notes covered. It becomes a lot less impressive when you realized these were pieces of music that I returned to every now and again over the course of many years that I spent a good deal of time on and were completely internalized. So, does that make me an excellent musician? In my opinion no it does not, merely a good technician that put in the time and effort. On the other hand, if I were ever able to rip off something like that off the top of my head while on stage with a jazz combo, that is a different story… and I probably wouldn’t be a computer programmer 
. That is the main reason where some of the guitar players that bill themselves as “classically trained” can play as quickly as they do.
All the jazz guys, guitar-gods, etc. have spent hours playing licks, doing studies like mentioned above, transcribing solos from other players and really learning the in and outs of their instruments. I’m sure Eddie Van Halen (and every 18 year old whiz) that can smash out Eruption, or Yngwie with his flurry of arpeggios, or Nuno Bettencourt playing Flight of the Bumblee have spent hours learning the techniques involved…. but is it something beyond what an average person can do if they spent the time? Again, I think it isn’t. As a weird example a couple of months back on NPR I was listening to a professor up in Canada that had built a robotic bag-pipe player that was only limited to the physical amount of time it took to vibrate the reeds in the bagpipe. The bag pipe robot was playing “Danny Boy” from start to finish in something crazy like 3 seconds. Is it true musicianship since no human could possibly play that?
So where does that musical magic happen where those “handful” moments exist? I think it’s when you have a player that has spent the time to perfect the rote technical mechanisms of his instrument (like a lot of the players mentioned in this thread) and is freed from the “thinking” aspect of music and he is with similar players in a live setting. The players can then start combining all the different things they’ve learned and studied over the years and collectively start melding that into new sounds. That’s the difference between listening to an awesome Jimmy Page solo on a Zeppelin album (of which there are a lot that only really good guitar players can play) versus watching a concert video of Zeppelin where all cylinders are firing with Page soloing, and you know that that energy can only be created in that moment with Page, Bonham, and Jones never to be repeated again. That is the true beauty of music.