He's going to lose because having the incorporation papers in the car does not mean he has the corporation in the car. I would argue that a corporation's physical location is its registered agent address.
The existence of the corporate veil, that shields owners from personal liability, is written into the laws that define what a corporation is and will survive no matter what happens with the corporate personhood issue.
The concept that corporations are people with rights that were originally meant for people comes from court precedents. Congress never passed a law saying that corporations should have free speech, and money is a type of speech, therefore corporations can donate to political campaigns. The courts decided that corporations are people, and decided that the Bill of Rights applies to these fictitious people.
"A corporation is an artificial being, invisible, intangible, and existing only in contemplation of law. Being the mere creature of law, it possesses only those properties which the charter of its creation confers upon it, either expressly or as incidental to its very existence. These are such as are supposed best calculated to effect the object for which it was created. Among the most important are immortality, and, if the expression may be allowed, individuality; properties by which a perpetual succession of many persons are considered as the same, and may act as a single individual. They enable a corporation to manage its own affairs and to hold property without the perplexing intricacies, the hazardous and endless necessity of perpetual conveyances for the purpose of transmitting it from hand to hand. It is chiefly for the purpose of clothing bodies of men, in succession, with these qualities and capacities that corporations were invented and are in use."
-- Chief Justice John Marshall, Dartmouth College v. Woodward, 1819
Corporations have rights because human beings have rights: they're just using the corporation to exercise those rights. But you'll note that there are some rights which aren't really transferrable, such as voting, and that corporations don't get to exercise those. Likewise, being eligible to be counted as an occupant of a vehicle for the purposes of carpool statutes... not really transferrable either.
Reasoning: if the car had been involved in an accident, who would be sued? Just the driver alone, or the driver and the car's owner?