The police thought it was the drivers cousin TJ, and according the daily mail report, he'd already shown them his ID, but they refused to believe it because they were convinced it was TJ, - as they kept repeating it - who I assume wasn't allowed to drive.
I agree that the driver could have got out of the car earlier, but having seem the reaction of the police office, I suspect he wouldn't have got a much better reaction - I suspect they'd have accused him of having fake ID, and hauled him off to the station anyway.