NASSAU COUNTY, Aug. 15 -- The claim landed at a law enforcement dinner in Long Island on Friday night: Donald Trump told a crowd of police officials at the David S. Mack Center for Training and Intelligence that after he finished defeating Iran, the United States would own one of the world's most contested waterways.

"After we finish defeating Iran, which is being very badly defeated, pretty soon I'll be declaring the Hormuz Strait a territory of the United States," he said to cheers from the room. Hours later, a senior White House official told reporters that Trump had been joking and had not discussed any such move with his advisers.

The gap between those two statements, a presidential declaration at a campaign-style dinner and its im...