I believe that the dealer may be right in this case. I have had 2 different cars with similar issue and both were the control modules. Fortunately for you there is a cheaper solution. I basic goggle search for Control modules will reveal places that will repair your module. we are here in Maryland and we use H&R. They repair all sorts of radios and control modules. It should cut your repair bill by about half to have your module repaired.
Technician
23 Years of Diagnostic Repairs, Former Snap-on Trainer