A reader had a provocative explanation, posted as an anonymous comment on the blog post on the Slavic tennis women mystery:
Soviet-bloc eugenics. If you look at the biographies of the Russian tennis players, like Kuznetsova and Petrova, they are the product of the marriage of two Olympic athletes.
Nadia Petrova: Petrova's father Victor was a leading hammer thrower, while her mother Nadezhda Ilyina won a bronze medal at the 1976 Montreal Olympics in the 400 meter relay.
Kuznetsova: Her father, Alexander Kuznetsov has coached five Olympic and world cycling champions. Her father's protégés include her mother, Galina Tsareva, a six-time world champion and holder of 20 world records, and Svetlana's brother, Nikolai Kuznetsov, a silver medalist at the 1996 Summer Olympics in Atlanta.
Think about it. The Communists selected hundreds of young male and female athletes to train for the Olympics, and located them at training centers. Inevitably, many of them married. And their daughters grew up to be some fearsome athletes too. The reason they never win is that they were raised to be athletes, not champions. In the US, it's the real competitors who rise to the top out of nowhere, like Oudin
The question still might be why is the advantage more pronounced in women than men? My amateur guess is that the Communists were much better than Capitalists in developing female athletes, since the former wanted to maximize Olympic medals (who cares if they are male or female?), while the profit motive reined in the latter, and female athletics just doesn't pay very well in the free market. This legacy may still matter even after the Communists (mostly) disappeared.