If you are a fan of Kubrick, conspiracy theories (or both), you probably know that there are people saying that the NASA was so impressed with his film "2001" that they hired him to shoot the landing on the Moon one year later the release of that film. Kubrick never confirmed or denied it, but he included this in "The Shining".
PD: Also, I love the "variant" of this theory that says that he was so perfectonist that he shot the fake landing on the Moon...on the Moon :)