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Track doesn't hold any insights into this matter. The track star knows exactly where he needs to go when the gun sounds but the baseball player has absolutely know idea where to go when the ball is first struck. The reactions we are talking about are not the burst-out-of-the-blocks kind, but rather deal with the issue of determing the velocity and trajectory of the batted ball. That part is very difficult and certainly varies widely between players.
One reason you have difficulty believing this is because you think that all major league centerfielders the best of the best defensively and are essentially the same in which case speed is going to be the overriding factor. This is not the case. Major leaguers, with the possible exception of catchers, are selected primarily for their offense, not their glove. I showed in another thread the speed scores for numerous full time CFs which demonstrated there is a huge variance among them in that regard. Some were in the 60 to 70 percentile range (or even lower); that is they were just a bit above average for a big leaguer. Now if speed is the most important skill for an outfielder and there is a giant gap between the fastest and slowest full time center fielders, then doesn't it follow that there are even larger variations in other important traits? Doesn't that mean that there are some regulars who get genuinely bad jumps and take poor routes? Look at arm strength. Throwing hard is definitely an asset for outfielders, but aren't there lots of them whole have noodle arms? You wouldn't argue that there is essentially no difference between Ichiro's arm and Randy Winn's, so why would you say that about a player's instincts?