Yup, that’s basically it. And I agree that it’s pretty obvious once you see it—the key is to notice that distance 2T implies that nothing other than X0 could have affected both of them. But man, when I didn’t know that was what I should look for? Much less obvious.
… I feel compelled to note that I’d pointed out a very similar thing a while ago.
Granted, that’s not exactly the same formulation, and the devil’s in the details.