Part of my job is managing component warranty returns for my employer, a vehicle OEM. I see this regularly, I can say with high certainty that the manufacturer paid for the repairs. If the dealer did this, he'd go broke. They work on razor thin service margins and are under constant pressure from the OEM to reduce repair times.

The dealer may have left you the impression that he paid the bill, but they typically won't even start the repair until they have approval for the repair work from the OEM. A large percentage of claims are just like yours, where the coverage is contested and the goodwill is taken care of by the OEM.