The flag is there all right, it was dropped by a satellite - piece a’cake, but the “cosmonauts” had landed in Burbank, where Mary Pickford once worked!
You are close. From my "inside info", the cosmonauts landed on Stage 47 - Universal Studios, Universal City, CA. The moonwalking however was filmed in nearby Paramount Studios - same place where Star Trek (original series) was filmed. In fact, Star Trek production had to be halted for some time while the 'NASA' team was out there getting their footages.