Jack was never going to take the car. His housemates thought he was a star for not accepting it, which would have resulted in the prize money going down to zero (or would it?), but I suspect he would have taken it like a shot if he was told that he wouldn't have to face his housemates and would just exit through another door when leaving the house. He probably just didn't want to face all the angry housemates if he had taken the car.

Jeez he's not that big and neither is the car that small.
