Nobody doubts that athletic abilities have genetic causes. Bodily shape is strongly influenced genetically, as, undoubtedly, are all manner of things like lung capacity, the properties of muscle fibers, reflexes, visual acuity, etc. I can say this with complete confidence because these traits have clearly evolved, and so must be under substantial genetic control. (Even so, careful attempts to find genetic bases for even very striking group differences in high-level performance fail to identify any.) On the other hand, it is plainly insane to suppose that athletic performance is not very largely learned, and a result of interaction with the environment.(Link courtesy of Marginal Revolution.)
To be really concrete, think about distance running. With practice, just about everyone can increase the distance they can run, the speed they can sustain, etc. Presumably there are physiological limits on what any one body can attain, even with an ideal training regimen, but performance (which is all one sees on any test) is malleable. Practice can take someone from being winded after sprinting two blocks to being able to run a marathon. Very basic physiological parameters, like the rate of oxygen uptake, demonstrably respond to training, and over a matter of weeks at that.
Of course, the flip side of this is that not practicing reduces ability, and sufficiently drastic lack of practice takes someone from being able to run marathons to being winded after two blocks. It is not enough to have practiced at some point in the past. There needs to be continuing practice, which means continuing opportunity and motivation, as well as sheer physical capacity. If we took a bunch of kids from an environment where physical exercise is discouraged, and make them run laps every day for a year, at the end of that they will (on average) be better at running than their peers. (They may have acquired other issues, but they will be better at running.) If we now return them to their environment, with a pat on the back and perhaps a souvenir pair of sneakers, is there anyone who doubts that in, say, five years most of them will be pretty much as sluggish as their peers? Is there anyone who would look at the result of such an experiment and conclude that exercise cannot, in fact, alter the ability to run?
Of course, not every kind of physical performance is as malleable as is distance running. No amount of training is ever going to let anyone hold their breath under water for an hour. Similarly, I do not expect any sort of learning will be able to alter some fairly basic aspects of the mind, e.g., to force the capacity of short-term working memory up to twenty chunks (rather than "the magical number seven plus or minus two"). We have evolved certain kinds of physical adaptability — feel free to speculate on why running might've been more useful than breath-holding, but not so useful as to be automatic — and similarly we have evolved some kinds of mental adaptability, but not others.
(On a related note, my friend A.'s most heartfelt piece of advice to young journalists is to take a good statistics class in college. I wish I had--too lazy, I think, to remedy this situation now...)