We cannot know for certain how Judge Cardozo and the rest of the court would have ruled in this case had the facts been different. However, it appears from Cardozo’s opinion that the decision would have been the same even if the person injured had been in the back seat of the car and had not been in privity with the manufacturer of the car or of the wheel.
privity: Privity refers to a connection or bond between parties to a particular transaction. Privity of contract is the relationship that exists between two or more parties to an agreement. (West's Encyclopedia of American Law)
The whole point of this decision was that there was no need for privity between the manufacturer and the person suffering an injury in order for the manufacturer to be liable. As it was, MacPherson did not have any privity with the company that made the wheel or the company that made the car (only with the dealer) and yet the Buick company was held responsible. If Buick could be responsible for the injuries of MacPherson, with whom it did not have privity, it would surely have been liable for injuries suffered by a hypothetical person riding in the back seat of the car. Cardozo’s opinion explicitly took note of the fact that the car was made to carry three people and that, therefore, there would be people in the car who were not in privity with the seller of the car.
All of these things show that Cardozo would probably not have changed his decision if the injured person had been a passenger in the back seat.