Not really, it's rooted in the Sino-Soviet Split, despite your "anti-Americanism" glue and mutual shared ideology (read: Communism).
It's not China claims to be true intentions, but rather what the perception by opposing party that ultimately matters. For instance, China perceived USSR as a "revisionist power" and "existential threat", and I'll bet a $99 dollars that USSR would deny those claims and claim China was the "reckless power" and "aggressor". Perception by the opposing party is ultimately what matters and drove the Sino-Soviet Split, not what one party exposes to be their true intent.
If there is an enormous economic and military disparity between China and Russia, then it's entirely possible, in fact, likely that Russia will percieve China as a security threat to Siberia, due to declining Russia population, climate change rendering natural resources more accessible, and opening of the Northern Sea Route between Europe and Asia.
Plans don't work out as perfectly as you describe. Using your logic, Joseph Stalin would have said to Mao Zedong:
"China has a "choice" (it's not really a choice) of being the right hand and trusted confidence of Soviet Superpower, or rather one of concubines of Americans' harem. Except the latter isn't even offer;"
Guess what, when China perceived USSR as a threat and US offered a quasi-alliance, then China became a quasi-ally of US as a counter-weight to Soviet Union.
Russia and China already tried an "Anti-Americanism" alliance, and Sino-Soviet Split was a result. Are you really going to discount a "Reverse Nixon" based on purely "anti-Americanism" alone?
Russia shares a heck of a lot more language, culture, and ideology with the West than China.
Then how do you explain the Sino-Soviet Split. If anything, US was an explicit enemy of China during Cold War, and USSR/China shared a mutual political ideology, yet a common enemy wasn't sufficient to prevent Sino-Soviet Split.