I purchased throughout the buying service last year. Here's what happened to us. We got a response back from more than one dealer. We went to one dealer, and they acted like they could get the exact car we needed could be obtained. What they were really trying to do was trade with another dealer who had the car and wanted to make the sale at their lot. We just happened to call the other dealer that was not a usaa approved dealer and found out they had the car we wanted. They agreed to the same price and used them instead. USAA still approved the loan. Hope that helps.
In my personal experience the loan is through USAA but it doesn't matter what car dealership you choose. I prefer to choose one of USAA's because sometimes they do have special rates and or incentives due to the relationship.
If you have a specific question (ie the loan and the dealer) I would encourage you to call in to the loan department and make sure.