The amount of the charge does seem to be over the top but consider this:
If you go to a convenience store and buy a 20oz bottle of Coke and pay $1.29 when you could have bought it at Wally World in a six pack for $4.90($0.82ea); Were you ripped off?
Directly from the benefits brochure:
"On occasion and whenever possible, we will make arrangements for the Member or Associate to purchase a tire(s) for delivery 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."
The "other fees" probably covers a multitude of possibilities including the tire dealer charging a higher price through GS to cover what he pays GS for the referral or making up the discounted service fee he gets from GS. Since you went directly he gets to look like the hero by charging his normal price because he didn't have to pay GS or discount anything.
Again, I think the markup is excessive but it is not an unusual business practice.