You aren't really purchasing the slingapp again; you're only reinstalling it. As long as your iTunes account is the same one that you originally purchased the slingplayer app on, it will verify it and automatically allow you to reinstall it without charge.
Apple had recently within the last 6 months or so changed that process in iTunes to show your apps as either installed or install if you've purchased it, but haven't yet installed it it. Maybe your iTunes isn't up to date and doesn't show you this, but it still shouldn't cost you anything to reinstall. You could always contact Apple just to be sure.