How to determine what is modifying com.apple.loginitems.plist?
The only other 2 locations I can think of that are Mac related and not within the app settings itself are /Library/LaunchDaemons (which you may have already checked when you checked /Library/LaunchAgents) and the preferences files for the app. If you have an appropriate application to examine them (like Xcode) you could take a look at:


~/Library/Preferences/com.slingmedia.plist
~/Library/Preferences/com.slingmedia.setupassistant.plist
~/Library/Preferences/com.slingmedia.slingplayer.plist


I personally do not have a slingbox or the app installed so I can't examine them myself but it would be a really 'crappy stunt' - as you put it so elegantly :) - if the app is designed to execute some code every time it launches to re-initiate the login item settings.