It's called "Bushing" and it's completely illegal. They are trying to defraud you.
They have something like 3 business days to get the loan approved and if they can't they have to call you back, you return the car, get back your downpayment and trade-in and the contract is nullified.
http://www.komotv.com/news/archive/4010596.html
Edit: Actually looks like that's applicable to Washington State Law at least. Dunno about your state.