C'mon sundialsvcs, pull the other one! Chairman Mao in China, Brezhnev in the USSR? Either of those guys would have absolutely loved to spoil the party for the Excited States under Nixon, if they were claiming credit falsely. They would have loved to trumpet the falsehood to their respective countries and warn them how they could 'never trust the west.' On the balance of probabilities, the moon landings happened.

They made enough fun of the US a few years later over Watergate, although I believe Nixon was told how their system could handle such problems. They did, too. [Tienamen Square].

My lasting memories of that was Time magazine (my Dad had a subscription):

1. A cartoon depicting someone lonely and dejected soldier retreating on horseback at dusk in a Napoleon-type hat & cloak, with the 'Nixon' caricature nose sticking out from under the hat. The place he was retreating from was called "Waterloogate."
2. The last Press photo I saw of Nixon before he resigned was of him addressing an auditorium, and the camera was right of stage, so you saw Nixon on the extreme left, the whole crowd, and this massive banner on two poles being held accross the back. It read "Impeach the <expletive deleted.>"