Strictly speaking, while what the Darius did may have been a bit of a jerk move, there's nothing against the rules about taking a kill. As long as it's still with the ultimate goal of winning the game, and it isn't done with the primary intent of griefing/harassing the teammate it's being stolen from.
Rage quitting a match on the other hand, is actually against the rules, and if your friend makes a habit of it, he will end up being punished by the LeaverBuster system. And I can promise you, if the Support staff don't remove a LPQ penalty for a player for a disconnect that was beyond their control, they sure as heck won't remove one that comes about because of a rage quit.
Though from re-reading your post, I'm confused. You said your friend threw the match, but then that the Darius blamed him for leaving? So did he intentionally feed and then quit? Or did he just quit? You should let your friend known to be cautious about things like throwing matches. More and more players are being punished for intentionally feeding lately, and those penalties start with a 14 day suspension.