Dealerships are independent business entities, and just like most people, the cars in their inventory are given to them on credit. So they must play by the creditor’s rules. Normally, if they sell GMs, GMAC would have provided the loan. If they sell Hondas, then Honda Finance Corp provided the loan. The creditor provides all the contract paperwork the dealership is allowed to use. Dealerships are NOT allowed to generate their own contracts if they are selling cars that are given to them on credit.
Since the vast majority of new car buys are done on installment contracts, generally the only type of paperwork available to the dealer is an installment contract. For the installment contract to be accepted by the financing bank, the customer’s FICO will have to be populated on the form. (This is typically systematic; if the form is sent with blank FICOs, it is automatically rejected without an analyst ever having seen it.)
So for a cash purchase, the finance manager would probably fill out the down payment as the amount given to them by check, and then the remaining monthly payments would be zero.
If the FICO comes in really low, and the customer is attempting to purchase an expensive car, the finance manager would probably reject the deal to to suspicion of fraud.
I have not seen a “lump sum” purchase contract for a new car… and if I did see one, I’d suspect the dealer fraudulently obtained the inventory. (Believe it or not, inventory-level thefts of cars from manufacturers is a very popular crime right now.)
In a nutshell, do not be surprised if a dealer wants to run your credit even if paying cash for a car. As long as the paperwork is handled above-board, there should be no fear of them having ulterior motives for having you go through the rigor marole.
FWIW, at the auto maker I work for, it is permitted for a credit analyst to do a Google search on a customer if the application is suspect or the info on the application isn’t readily verifiable.