Yeah, do that. There are ZERO laws that say a dealer can't refuse you service. Do you honestly believe that you can make them work on your car? Do you think dealerships haven't "fired" customers before? I know of a circumstance where a guy had bought cars from a dealer, but bought a truck somewhere else, then had a tonneau cover installed at his old dealer. There were problems with the tonneau cover and the customer flamed them on a survey. There were literally notes from the owner of the dealership that popped up in the DMS saying "PER (name retracted-but owner of dealership) UNDER NO CIRCUMSTANCES WILL WE DO ANY WORK ON THIS VEHICLE".
Most service departments don't really care where you buy your car, they want your service work. However, when a new vehicle comes out that is problematic and they could get flamed on a survey for a car they didn't even sell, attitudes change. Plus, with the current labor shortage, a lot of dealers are too busy for all the work they have anyways.
I love reading these posts "Why would they do that?". It's like I'm invisible. I've told you guys the problem, but just keep living in disbelief and asking the exact same question.