Yeah, the carrier doesn't have to do anything. The roofing industry is nearly completely unregulated. Did the roofer pull a permit? Did the inspection after it was done pass? Do you even require one where you live?
I'd call the main number and see if you could get another roofer to make the repair and have them pay the bill. That's what I did on the job I referenced earlier. It was the best way for them to shirk the Fix but pay the bill and not have the customer absolutely dEstroy them on social media.
If that fails, I'd have it fixed on your dime and chock it up to experience. I send my customer insurance, references, my Facebook page, my companies business page, my business page, and my business card has my photo on it. There is no way I'm walking away from an issue Or an unhappy customer. I want my customers to know that I am accountable and that what I do is not some side hobby. My customers are generally my own neighbors and I treat them as such.