I think they should replace it as well. Especially when they forced you to buy the tires from them. If they don't have the proper tools and training to do the job then they shouldn't do it.
I don't trust a dealership to do anything, but there are some things I just prefer not to do. When I was younger I tore into everything, fixed everything and often made my own parts. Now, I just don't have the interest in doing so. When I go to the dealership I just am afraid they will not do the same kind of work I would do. It goes back to the old saying....Be the job big or small, do it well or not at all.....if the job is once begun, never finish till it's done.