I think you're right about the citizens, but wrong about the stories we hear from our governments. There really was "the monster in the closet" with the Soviet Union. However, it was an independent press that included not only US reporters, but those of Europe and elsewhere in the world, who informed US citizens of the nature of the Soviet beast. Citizens of the old Soviet Union, on the other hand, had access to nothing but the controlled "news" provided by the state ministry of information.
It is not accurate to say that America is provoking the current tensions. A casual reading of international news will tell you that the tension is rooted in Putin's ambition. In my opinion, he very much wants to return Russia to the "good old days," when the KGB (his former employer) and the Communist Party ruled an expansive empire and threatened countries with seeming impunity.
That is my opinion as a citizen, and I have nothing whatsoever against the citizens of Russia.