I became interested about this subject after reading from this piece by Radio Free Europe https://www.google.com/amp/s/www.rferl.org/amp/30065499.html
No, the Soviet government did not support this idea. In all Soviet books, the flight to the moon was covered as a fact. The reason is that the Soviet Union censored various anti-scientific theories (with the exception of the humanities). After the union collapsed, censorship disappeared and people who had no experience to think critically began to believe in a huge amount of nonsense.