TPMS and Flat Tires

[dms489]

I had a flat Friday night that made a big hole in the tire. Being late, not thinking, I cranked up the flat fixer. Since the hole was big, nothing good, so I call for service. They towed the car to the dealership. Saturday, I was told they didn't have the tire, and would get it Monday. The car has done 5,000 miles. Today, they call - $200+ for the tire, $200+ to replace the canister and more to replace an inflator pipe. I'm OK with the cost of the tire, but Amazon has tire inflators for $40. Complete. $17 for a refill. Is there any reason I shouldn't tell them to keep the inflator, and get the inflator from Amazon? They should work OK, shouldn't they? ... and Oh, by the way, why would you sell a car that needs super duper Michelin tires without keeping the tires in stock in the parts dept?