Yup, that's absolutely true. At least, according to the press kit for The First People On The Moon, which further states:
It can be discussed endlessly if the Americans landed on the Moon or not. But "THE FIRST ON THE MOON" convincingly proves - Russian cosmonauts were the first there.
For the first time ever, the film reveals long suppressed footage of the Soviet space program, detailing how, in the 1930's, during the height of the Stalinist era, they sent the first man to the moon.
Okay, Amerikanski, the film is really a mockumentary [hope I didn't spoil it for you], but a lot of the footage is well faked and the movie is somewhat funny, in a grim Russian sort of way. Also, there is this to consider from the press kit:
The first cosmonauts showed in the film are not people only but a pig, a monkey and others.
Oh, and by the way, even though the Soviets weren't the first to land a man on the moon, they were the first to land an unmanned craft there. Don't believe me? Read about it here.
June 15, Harvard Exit, 9:00pm
June 18, Harvard Exit, 7:30pm