About Push Notification Rules in iOS

I’ve been using iOS for some years now and there’s a behavior regarding Push Notifications that I still don’t understand. When I launch an app for the first time, let’s say a game, and the system asks me “AppName would like to send you push notifications (Notifications may include alerts, sounds and icon BADGES. This can be configured in Settings).” I usually select DON’T ALLOW, mostly with games. Buttttt…. Apps can still generate Badges in their icons and list notifications in Notification Center. I must manually check the Notification Center settings to disable Badges for those Apps even when I’ve selected “Don’t allow” when asked. This behavior started happening to me since iPhone 4 with iOS4 and keeps being like that in my iPhone 5 with iOS7.

Any explanation?