Do they, though? That does seem to be the underlying assumption of this thread. I've seen a lot of people on this site equate having anxiety problems with being smarter. I have yet to see any evidence of this.
I think the idea is the that stupider people "think less," which is not the case. The difference is what people think about, and if all your thoughts are revolved around worry you are not really putting your thoughts to good use.
And then there's the other idea that if your smarter then that means you spend more time by yourself, and if you have anxiety you spend more time by yourself, so then the two must go hand in hand. Again, really not the case.
I've found that people like to look for the "good things" about having SAD or AvPD or whatever, which there really isn't. There aren't these underlying qualities that everyone suffering from these disorders have in common. Being smart is good, but having SAD does not make you smart. Being caring is good, being considerate, being thoughtful, being "deep," but none of them are the result (or the cause) of having SAD (or AvPD or whatever).
What the people on this site have in common with one another speaks more about what people who would join an Social Phobia forum do than those who have Social Phobia.