Tom Tunguz claims that this is the origin of the elevator pitch:
The term elevator pitch originates from the very first demonstration of an elevator with a safety brake. At the time, elevators were hazardous, routinely plummeting down shafts when their hoisting ropes fell, destroying their payloads. In 1852, Elisha Otis invented a locking system that would catch and secure plunging elevator. Unable to drive much interest in his innovation, Otis organized a demonstration in New York City. He stood in the elevator as an assistant severed the hoisting ropes and the safety brake engaged. Otis' innovation paved the way for humans to ride in elevators. Today, the Otis company’s products transport 7B people every three days.
If true, this is a more interesting tale than the story that I thought was the source: finding yourself next to your client CEO going up in the elevator and having 1 minute to sell your idea.