The only time Cutler was "seriously" injured against the Chargers was when he was with the Bears and he broke his thumb trying to make a tackle after throwing an INT.

So you might say Rivers celebrated him breaking his thumb rather than celebrated the turnover his team just got if you really wanted to push a false but possible narrative. Except, of course, nobody actually knew Cutler broke his thumb on that play until after the game. He played the rest of the game with it, didn't miss a snap. In fact, Cutler has taken every snap in every game he's started against the Chargers in his career.