I've admittedly not worked through Geroch's paper thoroughly myself, so I won't make strong claims here. But based on my understanding, I'd say that his assertion is a bit stronger than what you're suggesting here. He's not just giving a sort of meta-argument that "the space-time manifold of the universe must be consistent, so some mysterious effect will always stop you from killing grandpa".
Rather, his point is that your second theory (the one that you're adding to standard relativistic physics) has already been assumed to be causal when taken on its own (it must have a well-defined initial value formulation: that's one of his postulates). What he demonstrates is that putting the two causal theories together will still preserve causality. So when he says that you won't be able to use standard SR tricks to create closed causal curves, he really honestly means that any possible arrangement of the matter/energy content that could do that would be forbidden by the fundamental laws of the theories you're using. (Not just that it "wouldn't happen to work out".)
To phrase it yet another way, Geroch would say that you could not build a time machine in such a theory, not just that you couldn't use it to change the past in a meaningful way.
Rather, his point is that your second theory (the one that you're adding to standard relativistic physics) has already been assumed to be causal when taken on its own (it must have a well-defined initial value formulation: that's one of his postulates). What he demonstrates is that putting the two causal theories together will still preserve causality. So when he says that you won't be able to use standard SR tricks to create closed causal curves, he really honestly means that any possible arrangement of the matter/energy content that could do that would be forbidden by the fundamental laws of the theories you're using. (Not just that it "wouldn't happen to work out".)
To phrase it yet another way, Geroch would say that you could not build a time machine in such a theory, not just that you couldn't use it to change the past in a meaningful way.