Disagree.You're right, but they're both sick of the US hegemony and would be willing to work together to take us down first before they would decide what to do with each other.
It's not unlike the Axis during WW2, it's possible had they won they would have eventually fought a war amongst each other, but at the time they were allied to focus on taking down others.
They hate US hegemony but still don't trust each other enough nor hate the US hegemony enough to try a martial alliance against the USA and its allies. China would have to fight India and the USA at least on land while relying on *possible* suppkrt from a Russian military with extremely limited power projection capabilities. Nevermind that China still has yet to float a serious blue water navy itself.
Also, the Axis was an agreement between regional powers for regional hegemony. They may have had global ambitions, but those were still not entirely realistic and the scenario was reversed. They had more reason to trust each other and fight the hegemons than they did to fight/distrust the other members of the Axis.
Finally, the much more atteactive route to their current aims is grey warfare. Think little green men and martial harassment in the air and in the cyberspace. Both of these countries know that any other war against the current hegemons means annihilation, so why not take the low-risk, realistic approach to accomplishing their aims themselves?