I agree, it's a very cool study, and it would be a strange coincidence for him to "just happen" to have three super talented girls, at the exact same skill, and a rather esoteric one at that. But that alone will have a hard time settling the issue, simply because these things are inherently hard to settle. For example, this study may show that hard work and encouragement are the main ingredients, but that doesn't mean that certain amounts of talent wouldn't make it even easier. Maybe they would have been 2800 for example if they had "even more" talent. Or maybe not -- we can't really know, despite how much we may want to :)
But still, the study was quite a phenomenon, quite intriguing.
To be fair the "skillset" for chess is hard to list due to its complexity. You can't just chock it all up to "math, spatial relationships" or something like that. It's a bunch of skills all intertwined, psychological, practical (e.g. time management), mathematical, philosophical. Then there's your willingness to study for the game and persevere, which again can lead to the thought that women are more well rounded and don't consider putting the time in a good idea. Etc, etc, etc... :)
So it's kind of hard to pinpoint what's going on. I think social stuff, and indeed the psychology of stereotypes, has a lot to do with it, but does it explain the entire difference in performance? It's kind of a huge difference. We know for sure that it explains a fair portion, but to know for sure that it explains the whole thing? Seems like a really hasty jump to me -- it could be true, but to me there's not nearly enough information to feel sure about something like that. It's one thing to say the method of raising a child will influence them; it's quite another to say that it works like magic, that it is the only thing that can shape a person and everything else is just a really really clever illusion.
Well, the Polgár girls were raised to be geniuses. I believe it was Susan (Zsuzsa) who willingly went under brain tests and different exams made by machines in a documentary about this. They found there is actually nothing of extraordinary in her brain, it was all "just" the result of hard work and study.
Go and read their father's study, it really is worth it, how he explains the whole theory, as it was actually a theory of his, he wanted to prove supergeniuses can be raised with the perfect method.
So there's that. The behaviorists are somewhat right. Of course chess and all of these games require a fair amount of natural talent of all kinds as you said, but the "Polgár case" has lots of truth in it.