Apple is starting to remind me of MS.
Check out this inconsistency:
iOs used to allow effective blocking of Game Center.
The method was by logging out of your account within the Game Center app. This is followed by disabling changes to accounts, which prevents anyone from logging on. It is done by going to Settings>General>Restrictions, and disabling "Allow changes" for "Accounts".
On iOs 6, this prevented users from logging on to Game Center from within the Game Center app.
With iOs 7 however, there is a way in through the back door.
Users can still log in through a new Settings menu, under Settings>Game Center. So, even though they cannot login within the actual app itself, as the actual app does not allow you to sign in, they can circumvent that by logging in through Settings>Game Center, and then return to the app and play games etc.