As I read that, I felt it was a bit too strong - isn't the issue whether spacetime have an independent physical sense? I went back to the article, and I see that it starts "What is space? What is time? Do they exist independently of the things and processes in them?" As the argument starts with a manifold of events, an answer of 'no' to the third question seems reasonable to me (though I realize, from experience, that that's probably because I haven't fully grasped the argument.)
As far as I can tell, the article doesn't indicate any particular problem with the 'no' answer.
In the argument in section 10.3.3, don't you have to accept the reality of K(t) in order to see a paradox?
