I have heard this theory and I am more and more inclined to believe it.
Russia pretends on the world stage to oppose American interests. That gains them trust with enemies, such as, Iran and North Korea, and they gather valuable intelligence that they pass on. Plus Russia will never want to openly appear to be too pro-American, it's just in their nature. All I can say is, what you see on the surface may not necessarily reflect reality when it comes to Russian-US relations.
Shrewd comment. In the longer run, and Putin knows this, Russia is going to need the West just a whole lot. He'll need, at a minimum, good relations with the West to keep the Germans off his back while he deals with China and the Central Asian republics.
Most of his snit toward the U.S. reflects U.S. demarches from '90's policies put in place by Bush 41, specifically with regard to not moving NATO to the east (we weren't going to, and then we did, and U.S. troops are in Armenia).
What good proposing instead that some of those Eastern European republics follow a "Finlandization" policy instead, we can't know now.