This is non-sense, unless you are in the know about the Russia’s and China’s space programs. Their space technologies are generally behind the US (although China is working hard to catch up), and are less transparent, so we’ve heard more about initiatives such as SDA. That doesn’t mean their military space R&D are purely in response to US’s programs. Russia intended to use space for reconnaissance very early on after Sputnik [0]. They didn’t wait for the US to make a move first.

[0]-https://en.m.wikipedia.org/wiki/Zenit_(satellite)