I believe according to their brochure the only thing they are supposed to pay for is the service call which they should have done. It is your responsibility to pay for the tire and or rim.
Flat Tire Service
A service technician will replace a flat tire
with an eligible vehicle’s inflated spare, if pos
sible, or we will tow the vehicle to the nearest
professional service center. On occasion and
whenever possible, we will make arrange
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ments for the Member or Associate to purchase a tire(s) for deliv
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ery to the disablement scene. In these cases Good Sam Platinum+
Roadside Assistance will pay for delivery of the tire only, Member
is responsible for all additional costs including cost of tire(s),
mounting, balancing, other parts or labor, tax and any other
fees. Note: This benefit does not include seasonal tire changes.
Member or Associate is responsible for all parts and labor