Rear diff

Had the rear diff replaced on an 04 Wrangler, and 3 days later blew a tire on the highway (object punctured inside of tire then dislodged and broke drivers side mirror) and found fluid leaking in the wheel well. Shop inspected it and said there was a blown gasket, but claims it had nothing to do with the flat tire. Could a blown gasket cause an object from the rear diff to break off while driving and lodge in tire?