The depth of mistrust between the two was highlighted in the interview given by Hank Paulson, the former US treasury secretary, for my recent BBC Two documentary, How China Fooled The World.
The excerpts I am about to quote never made it into the film, because they weren't relevant to it. But they give a fascinating understanding of the complex relationship between Washington and Moscow.
Mr Paulson was talking about the financial crisis of the autumn of 2008, and in particular the devastation being wreaked on Fannie Mae and Freddie Mac, the two huge underwriters of American mortgages - huge financial institutions that had a funny status at the time of being seen by investors to be the liability of the US government, which in legal reality were not exactly that.
Here is Mr Paulson on the unfolding drama:
"When Fannie Mae and Freddie Mac started to become unglued, and you know there were $5.4tn of securities relating to Fannie and Freddie, $1.7tn outside of the US. The Chinese were the biggest external investor holding Fannie and Freddie securities, so the Chinese were very, very concerned."
Or to put it another way, the Chinese government owned $1.7tn of mortgage-backed bonds issued by Fannie Mae and Freddie Mac, and it was deeply concerned it would incur huge losses on these bonds.
Mr Paulson: "I was talking to them [Chinese ministers and officials] regularly because I didn't want them to dump the securities on the market and precipitate a bigger crisis.
"And so when I went to Congress and asked for these emergency powers [to stabilise Fannie and Freddie], and I was getting the living daylights beaten out of me by our Congress publicly, I needed to call the Chinese regularly to explain to the Central Bank, 'listen this is our political system, this is political theatre, we will get this done'. And I didn't have quite that much certainty myself but I sure did everything I could to reassure them."
In other words, China had lent so much to the US that Mr Paulson needed to do his best to persuade its government and central bank that China's investment in all this US debt would not be impaired.
Now this is where we enter the territory of a geopolitical thriller. Mr Paulson:
"Here I'm not going to name the senior person, but I was meeting with someoneâ€¦ This person told me that the Chinese had received a message from the Russians which was, 'Hey let's join together and sell Fannie and Freddie securities on the market.' The Chinese weren't going to do that but again, it just, it just drove home to me how vulnerable I felt until we had put Fannie and Freddie into conservatorship [the rescue plan for them, that was eventually put in place]."
For me this is pretty jaw-dropping stuff - the Chinese told Hank Paulson that the Russians were suggesting a joint pact with China to drive down the price of the debt of Fannie and Freddie, and maximize the turmoil on Wall Street - presumably with a view to maximizing the cost of the rescue for Washington and further damaging its financial health.
Paulson says this guerrilla skirmish in markets by the Russians and Chinese didn't happen.
But this kind of intelligence from China on Russian desire and willingness to embarrass the US in a financial sense may help to explain - in a small way - why President Obama shows little desire to understand Crimea as seen by Mr Putin.
And maybe if the US is being a bit more robust than the EU in wanting to impose economic and financial sanctions on Russia, that may not all be about America's much lesser dependence (negligible dependence) on Russian gas and oil.
There is a cynicism in the relationship between Russia and the US, being played out in the Crimean crisis, which is deep, rooted in history and shows that the triumph of capitalism over communism wasn't the end of the power game between these two nations.