No, the point is: The sphere doesn't care if you can prove if it is a sphere or not, it stays a sphere. If you CAN TELL if it is (or not) is a different matter entirely, so it doesn't work that you say "if and only if it is proven" when you make claims about something having a certain property.
i.e. Just because I can't tell if you have two hands to type this doesn't mean you don't have them.
"You have two hands if and only if there's a formal proof that you have two hands"
