Shell companies don't change anything. You can buy an aged shell, appoint nominee directors, etc. and it doesn't change the law. If anything, these things will only go to prove your intent to launder money and avoid tax if and when you're caught.
While that's not to say that aged shells, nominee directors, etc. don't serve a purpose for certain people in certain situations, a lot of this stuff is just designed to enrich the service providers through fees and provides very little meaningful value in terms of privacy and protection.
A lot of Russians use offshore structures to protect their assets from the state. Also, Russia has a territorial tax system under which nonresidents are taxed only on their Russian-source income. Many wealthy Russians live overseas, so if you make your money abroad and live abroad, there's nothing inherently illegal about keeping your money abroad if you're a Russian.
Basically, the reasons a Russian would go offshore are a bit different from the reasons an average American would.
Finally, in cases where a Russian was offshore for shady business, you should recognize that the long arm of the Russian authorities isn't that long. The US, on the other hand, can functionally knee-cap financial institutions anywhere in the world for refusing to do what it wants.
As evidence of this, consider that even Chinese banks will comply with US sanctions if they feel there's a risk to their US dollar operations:
https://www.bloombergquint.com/global-economics/chinese-bank...