That's silly. Our mobile service tech happily recommended a local shop when I asked who he uses. Some of the Tesla service departments will encourage you to use local tire shops for routine tire work, too, as it reduces the load on them.

A bigger issue is that some shops don't like to deal with the risks of lifting a car with a battery. Poor lift procedures can cost them a lot of money, and some avoid the liability. Most have reported success with Discount Tire, Costco, and other normal shops, though.