I have the integrated controller on my 11 GMC. Compared to the three past aftermarket controllers including the Prodigy that I have owned, none can come close.
I would suggest taking the time to sort out the problem. If the dealer stands behind his diagnosis and the brakes work fine on an aftermarket, I would tell them that(don't ask)you are bringing the trailer to the dealer and you want to see if the brakes work when attached to another truck with the integrated controller. You won't have to leave the lot to find out if they work on the other truck.