Two different points to be made in response:
(a) a player who IS injured, but is limping toward the sideline, SHOULD go to the ground. Why? Because as long as he is moving on his own, he is liable to be called for a penalty, like too many players on the field. If he really is injured, he and his team are allowed protection from that kind of penalty. That's why a coach telling an injured player (a truly injured player) to get down is a totally different thing than uninjured players flopping for tactical advantage (to slow down the opposing offense, or get some subs).
(b) Kiffin is not the inventor of the flop, no. It has been around for decades and decades. But last season he took it to a disgusting new level of unsportsmanship. THAT is why he (rightfully) gets so much grief. He embraced it so blatantly, and so frequently, that he set himself apart from others who use the tactic in a lesser way.