Did they pick the repair location or did you? Did they write you the check or the repair location?

If they picked the repair location then they would probably be responsible. If they wrote the check to the repair location then they may be responsible.

I would guess that they wrote you the check, allowed you to choose the repair location, making you responsible for the repair. They paid you for the claim relinquishing their responsibility and your claim-what happened from there is your business and your responsibility.