In this case Push is a function of MobileMe, which is a service... not an App. So while MobileMe might push out an e-mail to Mail.app, it is no different than any other e-mail it gets when the server is polled.
I'm not really sure what your complaint is anymore. "Push notifications" are an iOS feature, not an OS X feature. If you want a notification when you get a new e-mail, either visually scan the Mail.app icon for the red indicator or install Growl.