And they claim that the pricing is the same regardless of which purchase/finance method you choose. I suspect they are trying to blur some numbers. Anyone familiar with these finance models?

I had it explained to me that the "sales" price is actually a lease, which if you wanted to get for a cash purchase, you could enter into and then "pay off" as long as you keep the financing in place for a minimum of 4 payments. At that time you can "pay off" the car plus the sales tax on the original purchase that you didn't pay up front because it was leased.

Where I think it gets tricky is lease termination. I've been told there would be no additional fee for terminating the lease early. Would there be other differences between the amount you owe and what they would ask for to pay off the lease?

I just always assume that new car financing gimmicks are shady.