Look at who discount tire has working for them. The stores here have kids slightly older than hs age working. They could careless. Most people are not OCD about these things like most of us are on these forums
. Anyways, we had a local store rotate/balance tires. No damage to the wheels, but they did forget to reinstall 6 (plastic) lug nut caps across 2 wheels. Didn't notice it til later. Called them on it and they did order and send them to me.
I guess it's important to do a walk around with the mgr for any vehicle damage, then do an inspection prior to any tire coming off and after new tires installed but not mounted to car. If the car is < 3 years old and in otherwise pristine condition, I too would be pushing for new wheels, not refinished. Good luck!
One benefit of DT is you get lifetime (life of tire) free rotation, balance, and tire repair. I dont care much for the rotation, but the free balance & repair can be helpful.