That's a load of crap. I've watched a lot of space race documentaries and things about all of that, and the N1 moon rocket was far from ready even when 1969 came around.
In 1966, Sergey Korolyov, who was Russia's Von Braun, so to speak, died from a poorly performed surgury...
after that happened, the russian space program was never the same. They didnt even get any of the N1 moon rockets off of the ground until 1971, and the fuel that they were trying to use was way too explosive, and caused them to explode just seconds after takeoff. They also had way too complex of an engine system... 30 engines in comparison to the 5 used in the Saturn V rocket.
With what was found out in 1990, the only thing the soviets were able to beat the americans to with the moon race was development of a lunar lander.. which, looks remarkably similar to the LEM used on the apollo missions, but much smaller, as it was only made to carry 1 person. It was tested, and ready to go far sooner than the LEM was, but only because the soviets chose to focus on the lunar lander first, rather than the rocket to get the LK as it was called, to the moon, as the Americans did with the Saturn V
Just some sweet fun facts