On a rusty door at the top of a nine-story apartment building that no architect would admire, someone had scratched a declaration: “FALL OF SAIGON.”

Nguyen Van Hiep can still see it happening. On April 29, 1975, as South Vietnam’s government collapsed in the final hours of the war, he watched from next door as an American helicopter landed on the roof of the building’s elevator shaft, a space barely big enough to hold its skids.

A crowd of Vietnamese civilians squeezed their way up a narrow ladder to the military chopper, yelling and jockeying for position. An American with a white dress shirt ushered a lucky few onboard.

“Everyone was fighting to get up there,” said Mr. Hiep, whose father helped maintain the building known as the Pittman, where the deputy director of the Central Intelligence Agency lived and worked. “It was very chaotic, only people in the building could go.”

What he witnessed became iconic — and misunderstood — after a photo of the scene by Hubert Van Es hit the news wires with an editor’s incorrect caption saying that it showed desperate evacuees at the U.S. Embassy.