I would have them spin the rim by itself to make sure it is not out of round (radial runout) and that it doesn't wobble from side to side (lateral runout.) If the rim checks out there is a problem with the tire.

Was this tire on the front or back? If the wear is even on the one side and it is severe enough to cause lateral runout I would say you have a camber problem with your wheel alignment.

With a broken belt I would expect you would feel vibration through the steering wheel or in the seat of your pants. It wouldn't be a pleasant sensation either but it would feel expensive.