I was under the impression that the term "natural set" refers to things that normally come in sets, not things that only ever come in sets. Was I mistaken?
No, I don't think you were mistaken Soljasy. If sgcdonmai was right, I think that would have resulted in things like blue_eyes -> blue_eye (is that a disease?), because by his logic there are images of characters where only one eye is visible, thus "undoing" the "natural set."