I think that straight women generally do have higher standards for how socially skilled men are than straight men hold for women. I just don't think that this condition is caused by women being more socially savvy than men.

Perhaps the assumption that wasn't explicit enough in the way I said it, is that women are more socially savvy at relating to women than men are. (The term "natural" in PUA lingo more specifically refers to "naturally good at meeting/relating to women".)

It's pretty straightforward, though, how this leads to the PUA meme that "women are more socially savvy", when a more precise claim would be to say that "women are generally more sensitive to the social nuances of men's behavior than are the men performing those behaviors." The latter is the point the PUAs are trying to teach, namely that men need to learn to be able to see their own behavior from someone else's point of view.

(That the typical model for "someone else" used in such trainings is often "women of above-average physical attractiveness in bars and nightclubs" is a separate issue, which has spawned other debates here in the past!)

In general, problems occur when fairly narrowly-focused PUA concepts are interpreted without the aid of the background assumptions underlying them. Unfortunately, it's usually difficult for human beings to identify their background assumptions, because, well, they're in the background, not to mention being assumptions. ;-)