The anti-missile bases and technology are quantitatively and qualitatively utterly inadequate to make a flyspeck of a difference. Russia knows this.
They likely do. But as we've wasted well over $100 billion on our so-called "Star Wars" anti-ballistic missile system over the years, and even more money on the anti-missile systems we're developing with/for Israel, I'd bet the Russians fear the day that we finally get it working.
Consider that after the breakup of the USSR, Russia has engineered and deployed substantial new nuclear weapons and delivery systems. The US has not.
I think this is misleading. Of course Russia has developed new ICBMs. First, this ignores what may or may not have been in the developmental pipeline. But more importantly, it ignores that we did unilaterally break the ABM treaty and started deploying ABM sites and mounting systems on ships. To expect the Russians not to counter our aggression is to expect them to act foolishly.
Is it the US who is really the only problem here?
Considering the US has launched multiple wars of aggression since the breakup of the USSR, the US gov't wages blatant proxy wars, the US gov't ignores all int'l law dating back to the 1648 Treaty of Westphalia and claims a "right" to attack any country even if we have not been attacked first, and considering things like we have used flat-out torture as a national policy and spend almost 1/2 of the entire world's military spending, the US gov't may not be the "only" problem but most definitely our gov't is the largest and most aggressive problem country in the world.
Not surprisingly, but still sadly, it's not just me saying this; in one Win/Gallup International survey of people in 65 countries, the US is seen as the greatest threat to world peace.
"The organization has concluded that the United States is now the principle violator of human rights and freedoms worldwide." -- Amnesty International's annual report on human rights.