The country didn't make the claim; some in government did.
Armstrong & Aldrin: "I don't remember seeing any stars," which was consistent with the high quality, Apollo 11 Hasselblad photo imagery. And yet, the Chinese camera had not trouble whatsoever seeing the stars which were always there. Faking the constellations was simply too difficult for NASA and/or Stanley Kubrick. If star positions were in error, the entire operation would immediately be seen for the fakery it was.
There's no moisture in the lunar regolith to allow or cause it to cohere, so as to confirm Armstrong's classic first footprint. (See below: cleats/heavy treads were hardly necessary inside the Apollo 11 module as it stayed within Low Earth Orbit.)
Armstrong's lunar footprints in dry, dusty regolith would have looked more like this (if they'd been real):