There's no truth, it's Soviet propaganda at best.
The Soviets were very much engaged in the space race and the race to the moon. They developed a massive rocket at great expense (the N1) with no other purpose than to reach the moon.
They developed a full architecture of spacecraft and launchers for manned missions to orbit and land on the moon. The Soyuz 7K-L1 (Zond) design was intended to perform a manned circumlunar flyby. Several unmanned launches of this spacecraft were conducted using the Proton launch vehicle and at least one was attempted (but failed) with the N1. On one mission (Zond 4) the capsule was launched to a 354,000 km apogee orbit (which is very close to the distance of the moon and had it been launched toward the moon it would have orbited it), but due to a failure with re-entry the capsule was lost. On another mission (Zond 5) a capsule containing live animals (including tortoises) was put into orbit around the moon by a Proton rocket in September of 1968 and returned to Earth (the first vehicle to do so).
Additionally, there was the Soyuz 7K-LOK lunar orbital spacecraft and the LK lander. These spacecraft were designed and built and ready to be put into orbit. The design was simple, the LOK and LK would be launched together, after entering lunar orbit a single cosmonaut would spacewalk from the LOK to the LK then ride the LK to the lunar surface (using a disposable retro stage for most of the deorbit and landing thrust), after exploring the lunar surface the cosmonaut would return to the LK, blast off back into lunar orbit, rendezvous with the LOK and spacewalk back into it for the return trip to Earth.
Due to the failures of the N1 rocket program (which saw 4 launch attempts and 4 failures, some of them quite catastrophic) neither a manned Zond nor a manned LOK/LK spacecraft was ever launched, either into Earth orbit or toward the moon.
Nevertheless, the development of the hardware and the timing of the program developments makes it abundantly clear that the Soviets were quite active participants in the race for the moon. Every single N1 launcher carried an unmanned Soviet lunar program spacecraft, either a Zond or a LOK/LK.
Prior to a 5th attempted N1 launch in 1974 (again with an unmanned Soyuz 7K-LOK and an LK vehicle on a planned fully automated lunar orbit and landing mission) the program was cancelled. After which it was quickly mothballed, hidden away, and disavowed. Since much of the work on the components of the Soviet moon program was heavily obfuscated (e.g. semi-random part numbers) many workers didn't even know what they were building, and very few people had full knowledge of the program. But much of the hardware still exists and after the end of the Cold War many Soviet records detailing the program have become available.
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Yes and no. It depends on the point in time you are asking about.
For quite a while the soviet space program was aimed at doing science while not costing too much. They got their funding due to the "dual use" nature of giant rockets, i.e. as ICBMs. But as the world started to notice, the political leadership quickly figured out the propaganda value of their nation's success in space. The space program was expanded and moon landing was tentatively planned for the mid seventies.
Then American president Kennedy gave a speech about landing on the Moon before the en of the sixties. Now, the US hadn't actually achieved all that much and their progress didn't look quick enough to manage such a hugely complex feat. So the Soviets didn't take this speech seriously. American politicians were known to promise lots of things without any intention of ever doing anything.
But what they didn't know is that NASA had been working on a Moon landing for a while and Kennedy had been given a detailed presentation about the plan shortly before giving that famous speech. So a couple years later NASA suddenly starts launching the Saturn family of rockets several times a year. This came completely out of the blue, because NASA had been working on these rockets even way back when the Mercury and Gemini programs were just getting started. The US government also spend a huge portion of the federal budget on this.
So the soviet politicians became worried and ordered their space program to also land on the Moon within a few years. But that was practically impossible to achieve within such a tight budget and schedule. One of the biggest hurdles was that the SU did not produce a rocket motor that came even close to the F1 engine's performance. The soviet philosophy had been to mass produce proven engines and to just cluster them together for more performance. Unfortunately the thrust necessary to launch even a tiny mission to the Moon (and back) necessitated a ridiculous number of engines, hence the N1 rocket.
The soviets actually made good progress on the N1. Western commentators often point to the frequent failures but that standard fare for the soviet rocket engineering process. They just flew it and examined the wreckage to find the areas they needed to improve. This system worked perfectly when you have hundreds of relatively cheap engines coming from assembly lines. It seems likely that the N1 could have been made to work reliably, had the budget or timetable allowed it. The other parts you need for a Moon landings were engineered as well, though they were only ever tested on unmanned flights. Because when they saw the Americans continuing to casually send people to the Moon for a couple of years, while their own rocket engineers only promised a lot but had not delivered yet, the soviet leadership killed the program and claimed they never targeted the Moon anyways.
TL;DR the soviets wanted to land on the Moon at some point but they didn't think they were in a race until it was to late to do anything about it.
The fact that Russia expended so much money and effort on the N1 program would seem to indicate that they were interested in the moon. Perhaps just not as much as the US. Given that each attempted launch (both for the N1 and Saturn V) cost about half a billion dollars, it's pretty understandable that they refocused their efforts on space stations.