Oh, I think I see your point now. But I think it's a weird argument, to be honest.

I suppose the fact that it's Peggy and Victor who are running that protocol is simply irrelevant. They're talking about that value of x after all, and nothing related to that topic is revealed beyond the proof of the fact that Peggy knows it. If she'd appear in person, wherever she wears a red shirt or a white one would be might be considered "information" but it would be completely out of scope.