From what Capers said on the radio one day is that he called the type of play: run or pass. Palmer would pick the play itself based on what he thought would work the best.
Then after all of that Carr still has the option of audiblizing the play. I don't know if Carr has permission to go from pass to run, but certainly he can pick a different pass play, put a receiver in motion, have DD run to the opposite side or call a specific route. I doubt Carr does a lot of complex audiblizing. I rarely see a Texan receiver go in motion.
Even Peyton Manning doesn't have complete autonomy. He gets to pick from three different plays when they call one in to him.