In fact, the number of deaths in Russia is under 1% of the number of confirmed cases. In the US it's well over 5%. Does drinking lots of vodka result in better outcomes? I can't think of any other reason.
While the average Russian might agree with your reason, I can't see anything wrong with the Russian to date numbers:
April 21 cases = 52763 (-21 days)
April 28 cases = 93558 (-14 days)
May 12 deaths = 2116 (2.3% with average 14 days to death, 4% if you assume 21 days to death)
The number of confirmed cases always undercounts the number of infected. Apparently, even the most diligent countries detect only 50% of infections. And at least in in the early stages, most are busy trying to ramp up their tests to find the existing cases, so you would expect undercounting to be much worse. So the Russians appear to be taking this far more seriously (adding 11,000 positive test results each day) than some of their European neighbors did .
The US as a whole is too far out of control for the positive tests to have much correlation with actual infections:
(From state summaries, less than the accepted national numbers)
April 20 cases = 775850 (-21 days)
April 27 cases = 982668 (-14 days)
May 11 deaths = 74731 (7.6% with average 14 days to death, 9.6% if you assume 21 days to death)
To match other countries who excelled at testing in the earlier stages, you could safely assume the US should have recorded at least 3 million cases by now. That suggests that maybe 8 million people were infected, based on a significant chunk of those being asymptomatic.
Of course, the US healthcare system is easily the worst in first world countries when it comes to epidemics, so you might be justified in assuming that lots of people died without even seeing the inside of a hospital.