Just getting all the facts here.
1. New Tires were purchased
Q. Were they delivered directly to the garage?
2. You inspected the car prior to taking the keys
3. You informed the front desk of the damage - prior to taking the keys
4. They were willing to repair the tire
5. You requested a new tire
Q. What did they tell you when you asked for a new tire?
Assuming that the above is true, have you contacted tire rack? Most of these places have a contract with tire rack at which point I am sure tire rack has more pull than you do.
If you haven't done so already, contact tire rack and explain the situation and that you've requested a new tire but they are giving you the run around. A decision should have been made on the spot, you are going to tell me no manager was on duty?