Aarons419,
Please ignore what most have said about this topic because I assure you they are not in the industry and really don't get the in's-and-outs of how a retail auto finance contract works.
First off, I am manager at and Audi dealership in SoCal and I did F&I for many years. Before you start talking attorney and what not, make sure you check the laws in your state regarding this situation. It sounds to me like the dealership will do everything it can to make sure this truck stays on the road. Trust me when I tell you they gain nothing by the truck coming back to them.
For example in my state of CA. It is not illegal or immoral to run someones credit, make a decision based on what we think the approval will be based on the credit criteria and allow them to leave the lot. We have to do this every Sunday because sometimes its dam near impossible to get an approval from the bank until Monday.
I can also tell you that on a CA 553 retail contract, every customer signs a box that says the dealer has the right to rescind the contract. Don't worry about the money, in CA it would be illegal to keep the down payment, and I'm sure AZ has something similar on the books. I know most will blame the dealer for saying hey your approved, but they don't speak for the bank, they can only go off of past history with the bank and make a judgement call.
To give you an idea, I've had a few people in the past that I never in my life thought Audi would turn down but they did for ******** reasons. We discounted the car, used every last bit of rebate and still couldn't get it done. My best advice to you would be check with USAA because your military, and please don't lose sleep over the down payment, I would bet the farm on you getting it back.
Dealerships are in the business of selling cars, not selling them and taking them back. I won't get anymore into the nuts and bolts of this whole thing, but if you need any advice P.M. and I will try to help you out the best I can.