[Oddball]

This is either an old scam or they genuinely were careless. Either way tell them to go f-themselves. Either they honor the financing they gave you on sale day or give you back your car and the down payment.

If they were not in their regular offices they should have people able to qualify you for a loan or not on hand for it. They baited and switched you to get the sale as someone pointed out. Now that you have the car you are more likely to do a lot more to keep it than if you had to do the same up front.