Thank you for a correct statement of the problem which indeed gives the 1/3 answer. Here's the problem I have with the malformed version: I agree that it's reasonable to assume that if the children were a boy and a girl it is equally likely that the parent would say "at least one is a boy" as "at least one is a girl". But I guess you're assuming the parent would say "at least one boy" if both were boys, "at least one girl" if both were girls, and either "at least one boy" or "at least one girl" with equal probability in the one of each case.

That's the simplest set of assumptions consistent with the problem. But the quote itself is inconsistent with the normal rules of social interaction. Saying "at least one is a boy" takes more words to convey less information than saying "both boys" or "one of each". I think it's perfectly reasonable to draw some inference from this violation of normal social rules, although it is not clear to me what inference should be drawn.