Americans were ready for the famous flag-raising photo, but many got the wrong impression from the Feb. 23, 1945, image.

The image, captured 53 years ago this weekend during the Vietnam War, galvanized the anti-war movement in the U.S. But a new documentary raises questions about who was behind the camera.

On Friday, the World Press Photo Foundation, a prominent international nonprofit, weighed in. It said that a monthslong investigation had found that two other photojournalists “may have been ...