I don't think Drew's ego would let someone else play cop with his badge. Also, if he did not want to be recognized, why flash anyones badge at all? If you don't want to be recognized or remembered, you don't go around cutting off hazmat trucks at a busy truck stop, and you don't have an angry encountr in which you flip off the driver and flash a badge.
Back in October, Drew still thought he was bullet-proof. He was not afraid to break the rules because until then, Drew had always gotten away with anything he did...including murder.
Susan