At the same time they were playing up their successes, Soviet propaganda folks were also very busy hiding their failures (missions only got a name/number if they succeeded) and
erasing cosmonauts if they washed out of the program for any reason. So, perhaps a liar assumes the other guy is also lying? The counterpoint being that the US launched from a publicly viewable location and every launch failure was witnessed by hundreds of spectators, as was every successful launch.