This has been nagging at me for a while, so I thought I'd try to set the record straight as best I could.
The Corbis photo above (also see Getty Images photo) is from President Kennedy's first State of the Union speech on January 30, 1961. Notice the flower in the lapel of House Speaker Sam Rayburn, seated in the back right (and which is visible in this footage of the speech), and the diagonal design of Vice President Lyndon Johnson's tie. (Click here for the January 31 edition of The Milwaukee Journal, which used a similar photo in which Rayburn's flower can be seen.)
Now compare that to the Corbis photo above, from Kennedy's speech on May 25, 1961, in which he talked of landing a man on the moon by the turn of the decade. Speaker Rayburn has no flower in his lapel, and Johnson's tie is of a different design. (Click here for footage of the speech, and here for the May 26 edition of the Youngstown Vindicator, where a close-up photo of Kennedy -- and Johnson's tie -- can be seen.) Also note the difference in the positioning of the smaller microphones in front of Kennedy.
I often see photos from the State of the Union speech used to illustrate the moon speech, typically the photo at left. This includes the JFK Library (click here), NASA (click here) and The New York Times (click here). (After communications with The Associated Press, the news agency changed its caption information.)