When I brought my 2002 Santa fe in with a slow leak in one tire, the tire tech refused to repair a thorn puncture in the sidewall of the goodyear radial tire. (11,000mi.of use).I had to purchase another tire for $87 difference. Was this justified?
Yup…If the sidewall is damaged it CANNOT be repaired. It MUST be replaced.
That happened to me when I bought my 2007 Yaris. I had about 30 miles on it and got a flat tire from a screw that entered into the sidewall. I had to buy a new tire.
So I looked at the bright side; I didn’t have to worry about having one brand new tire and three older tires with more tread wear on my car.
Your situation isn’t much different than mine.
Bad luck, but it could have been worse.
Make this one more vote for agreement with the tire tech.
In reality, he is potentially saving your life since sidewall punctures cannot be safely repaired. If you do find someone who agrees to repair it, that person is ignorant of the basics of tire safety because the structure of a tire is permanently damaged by a sidewall puncture. While it would probably hold air pressure (at least in the short term) it would inevitably suffer catastrophic failure at high speed, and that type of situation is frequently the cause of very serious accidents.
Count yourself fortunate that this tech knew his business.