First, AFAIK Bela Karoly (sp?) is not a Communist, and even if he were it would likely have no effect on his ability to coach gymnastics. If you feel like Communist-bashing, take it to GD or the Pit.
Second, Nadia has been retired from competetive gymnastics for quite some time, so her experiences with a younger Karoly may not be relevant.
Third, I believe Karoly was himself a competetive gymnast in his younger days.
Finally, someone who lacks the ability to do a particular thing may still be capable of explaining how to do the thing to another. In the case of gymnastics, a coach can certainly explain how the gymnast can improve, for example, body position to increase or decrease rotation, appear more aesthetically pleasing, etc. If one were to accept your logic, the only people who could coach sports teams or individual athletes would be chamions of the sport and simple observation shows that to be wrong.