On Wednesday, Brazil’s Supreme Court decided to release Turkish-Brazilian restaurant owner Ali Sipahi, after he was arrested last month and made the subject of an extradition request from his country of origin. His initial detention thrust Brazil into the middle of a conflict between the Turkish government and the opposition Hizmet movement—but it is unclear exactly as to how Brazil benefits by getting involved. Mr. Sipahi was arrested by the Federal Police on April 5 after Brazil received an extradition request issued by the Turkish government,...