IMO it was Kubrick trying intentionally to fuck with the moon conspiracy people... none of the shots in any of his movies are by accident. (although the carpet could be going a little too far)
After all why would Kubrick try to inform the public in a way that is obvious to people who already know about it (ie the moon faking authorities who on seeing this movie would immediately understand its message and reprimand him) whilst simultaneously be difficult for those who are skeptical about it to get the message?? if he wanted to reveal his cooperation in some faking exercise why not just come out and say it?