I did what you said and here's what I got...
Balloon Tray Notifications...
Display system tray notifications.
Display tray notification about update
Display tray notification about scanning
Display resident shield related tray notifications (automatic action)
Display state change notification [this one is unchecked]
Display E-mail scanner related tray notifications
They are all checked except the State change notification. Does that help?
Those items shouldn’t have anything to do with the program accessing your internet connection.
Are you sure it is AVG that is the culprit? You may have some other program that is pinging constantly, etc..
If you have broadband internet, you will get that, as your cable/dsl modem checks the ISP connection.