I think it is crazy that a dealer won't balance your tire. I had no problems getting my local Honda dealer to balance my tires a couple of years ago. I did not purchase my tires from them- (saved alot of dough buying them on line)! However, they did mount them. Is your dealer mad that you did not buy the tire from them, or pay them to mount it??
They did have a sign that said they would not mount tires purchased outside of the dealership. Mine were already mounted. I just wanted the balance. No big deal for me if that is why they turned me away. Next time I see them might be to buy a Honda Monkey. I can skip everything else. I do as many of my own stunts (maintenance) as possible.