So here is the Rest Of the Story:
Right after the sale (i.e., Friday night), I tried to contact Suzuki Customer Relations, but they were already closed. I did fax them my question, along with a copy of my sales contract. I also sent a question (not a complaint) to the Illinois attorney general.
Saturday morning, I spoke to the dealership's sales manager. He gave me a copy of the title transfer, which correctly shows the car as New, and also let me watch while an employee entered my car into Suzuki's warranty system as a New car. With respect to the contract itself, though, he said that he was merely doing what the dealer's lawyers told him to do. I replied that I still needed to find out what Suzuki Customer Relations would say.
On Monday afternoon--since I had not yet heard from Suzuki Customer Relations despite my Friday night fax--I called them. They initially started to give me a disheartening line about dealerships being independently owned, but after looking at my sales contract, the rep said:
Although the sales contract has the term "used" in one or two places, that is not crucial; the contract is still acceptable (though unusual, if only because most buyers utilize some sort of financing). However, the contract has some specific waivers and disclaimers which I should not have been told to sign and initial. He gave me the name and number of the dealership's owner, and said I should ask for a reissue or amendment of the contract without any signature or initialing of the inappropriate clauses. He specifically gave the hypothetical example of a new car purchased with a scratch (presumably from transport or lot-sitting) that the dealership should fix.
I called the owner's number, and his assistant took my information. Within minutes the same sales manager with whom I spoke on Saturday called me back and offered to print a new contract, with no signature or initialing of the disclaimers, and to shred the old one. I agreed, and that was what we did.
I now suspect that this sales practice may be a reaction to fraud perpetrated on the dealership in the past. It is, frankly, all too easy for a new car buyer to get a scratch on his car (due either to fault or victimhood), and then come back to the dealer claiming that the scratch was already present at the time of purchase. Perhaps the long-term solution is some kind of walkthrough as part of the car-buying procedure?