That's not what's being said. The fact is GR cannot explain why these two particles will suddenly start moving toward one another. All I've done in this simple thought experiment is eliminate every other externality.
The key point here is GR doesn't explain why curved spacetime causes objects to move. It only says that the movement can be modeled by curved spacetime. This thought experiment was just a way of expressing that.
Which is all to say GR doesn't explain what gravity is, it provides us a (complicated!) set of equations for determining an object's motion in a gravitational field. In my mind that's a fundamental shortcoming of GR as it was a fundamental shortcoming of Newton. NEITHER of their theories even tried to explain what gravity was, they provided a mathematical model for describing the effects of gravity. Newton's was good, Einstein's is better - but neither tell us much about gravity itself.
OTOH, quantum gravity tries to tell us what gravity is, but that has run into issues. Not only is it going to take someone of the caliber of Newton and Einstein to figure this out and people like that only come around every few centuries, but we have to have the means to test the theory. We have several theories, but we don't have the ability to test which theory is correct. We simply don't know which way to go.
Anyway, all that is to say GR is incomplete - and we know it.