The climax explains everything: Leonardo was indeed a US Marshal. His wife with suicidal tendency kills their children and he in turn kills his wife and sets their apartment afire. He is admitted to the mental hospital at Shutter Island. He escapes from the hospital. His doctor goes and brings him back to the hospital by saying that Leonardo is his boss and both are deputed to investigate a case relating to a missing patient from that hospital! That is the opening scene of this fantastic psychological thriller. This is my understanding of the story!