From the detailed policy PDF
"Flat Tires
In some markets, our trained roadside assistance providers carry a limited number of loaner wheels to quickly
replace a damaged wheel or tire. Service Centers may repair or replace your damaged tire at your cost. Please
make arrangements with your Service Center for this service. Pricing and availability is subject to change based
on location. Loaner wheels must be returned to the Service Center within three days or an agreed upon time
with service which will be exchanged for your original wheel.
If a loaner wheel is not available, transportation services will be provided to the nearest Service Center or
other location, so long as the desired destination is within 50 miles (80 km) of the vehicle’s current location.
You are responsible for transportation costs beyond this distance, or for any subsequent transportation costs."
So i read that as if you are not within the service centre area (where they might have loan tyres available).
They will at least tow you up to 80km to a tyre shop where you should be able to get something suitable.