It is interesting to note that the Chinese are apparently at least exploring the idea of denying overflight rights by satellites.Since the US Senate hasn't ratified the UN Convention on the Law of the Sea, we don't have that forum in which to complain about China abusing its territorial limits.
This is not a formal declaration, at least not yet. On the other hand, it WOULD fit with Chinese writings about legal warfare. Thus, one could imagine them bandying and floating such ideas, and in event of a crisis, pushing the idea that one does NOT have the right to freely overfly (in space) another nation for the conduct of "unfriendly" acts such as espionage (i.e., intel-gathering).
A version of this is being pushed in Chinese actions towards ships like the USNS Impeccable and Victorious, which were operating in China's Exclusive Economic Zone but NOT their territorial waters. According to the Chinese, such ships, engaging in espionage activities, are prohibited from operating in Chinese EEZ waters. (This may also have been the basis for intercepting the EP-3, 9 years ago, leading to the aerial collision between a Chinese fighters and the US aircraft. I don't recall off the top of my head.)
Regarding space, physics being what it is, for Low Earth Orbit you eventually pass over every part of the earth. I suspect that when the Chinese become more dependent on space their tune might change, but it is an interesting situation. If China is going to claim that artificial space objects may not pass over China, and enforces it, space exploitation is basically over. There goes everything but geosynchronous orbit items. And geosynchronous is about communications and some weather watching. Maybe some other systems is out there, but a quick Wikipedia search did not turn it up.
But, does this Chinese view conform with the Outer Space Treaty? Probably not.
An interesting future is ahead for us.
Regards — Cliff