The context is about the vertical extent of the national borders, not the edge of space.
Who says the vertical border ends with the edge of space? Once again, the vertical extent is not defined. Say, tomorrow they come up with a Skylon-like contraption that will be used in civil aviation. That would give a reason to the national governments to redefine the notion of "airspace".
> Anything orbiting multiple times is in space, and nobody will argue.
And how do you know that? Once again, with the example of China, nobody could come up with counterarguments precisely because it's undefined.
But those heights are well below the height you need for a stable orbit.
Anything orbiting multiple times is in space, and nobody will argue.
So in the context of satellites, you're wrong.