These situations are not even remotely comparable.
The fraction of Americans who abuse opiates is tiny compared to the percentage of Russians who abuse alcohol.
As a rough approximation, about 2.5 million Americans have an opiate abuse issue in 2016[1], out of a population of 319 million. This is about 0.8% of the population.
Statistics from the Soviet Union are hard to find due to the government's indifference to the problem, but even official news sources -- which routinely greatly underreported the true magnitude of social problems -- put alcohol abuse rates at 19% of the population.[2] Also note that the amount of drinking you have to do to be considered "abusing" alcohol is far, far greater in Russia than in the US.
[1] http://www.asam.org/docs/default-source/advocacy/opioid-addi... [2] http://alcalc.oxfordjournals.org/content/34/6/824
People just don't have enough to do otherwise.
And even deeper down, it's a means of survival. The safety net here has pretty much disintegrated since it began to be dismantled in the '80s. A lot of people in the US haven't saved enough for retirement considering this new reality... they haven't even saved enough to get them through a few months of unemployment. There's a loss of hope in rural America now in places where it can be very tough to find decent paying work. It's starting so show up in a decrease in lifespan and in many ways it's very similar to what happened in Russia when the Soviet Union collapsed. The drug of choice there was/is alcohol. Here it seems to be prescription opiates (in addition to alcohol).