This is not a weak argument. It is real. From what I have know, the Push Notification goes from the service's server, then to iTunes store server (to verify that you have legitamate copy of the app) then to your iPhone or iPod touch. However, too much notification goes in, it will crash iTunes, since it goes through iTunes.
The app store update is done via push notification. Many people do not realize this, but after couple of days, if the user has not opened the App Store.app on their iPhone or iPod touch, the app automatically checks for the update via push notification service. The App Store.app push notification needs to go through iTunes, since apps are found in iTunes, but also to verify that you have legitimate copy of the apps. This is how you get the app number thing on the app store.app icon sometimes.