Atwood doesn't seem wrong or particularly unclear to me. If you "met someone who told you they had two children, and one of them is a girl", then presumably we should imagine this person saying: "I have two children and one of them is a girl," and not "I have two children, X and Y, and X is a girl." Obviously in the first case, we don't know if it's X or Y that's the girl, so the set of possible worlds is [(X-G & Y-G), (X-G & Y-B), (X-B & Y-G)], so we get the 2/3 answer. But maybe other people don't share my linguistic intuitions...
If I met someone who told me "I have two children, and one of them is a girl," I would be pretty sure they have one girl and one boy. If they had two girls, they would have said "I have two children, and both of them are girls." So the English statement has some implicit information. On the other hand, if I were given a riddle with that statement, I would know the implicit information may be intentionally misleading. In this case, as Paul Buchheit says, the statement does not have enough information.
