I agree with that. But I'm questioning the reasoning at the end of the story that they better not shut off the simulation, implied to be for their own sake. The observation that their higher-level reality counterparts will likely choose to shut down the simulation exactly if they do themselves, but the protagonists' choice doesn't influence that.
IMHO, the entire point of the story is that causality has become twisted into a counterintuitive shape.
From a naive literal point of view, no, the universe above theirs is independent. Diane's hypothesis/theorem is that, because their universe is at or near a fixed point, they have in effect invented a way to have unlimited control over their own universe. While there is no causal relationship from their universe the one up the chain, the symmetry implies their actions are mirrored.
I've read some of this author's other works. He likes playing with paradoxes like this. It's a twist on causality (and free will), inventing a new way for your actions to have an impact on the universe in the absence of a traditional causal link. It's pretty damn clever.
They are making decisions in the presence of the knowledge that essentially identical "god" agents will be making decisions based on the same information and the same mental states, and that the "god" agents' decisions will impact their own existence.
If at any time they were to "choose" to shut down the simulation, it can only be because the total state of the world, including their sense-data and internal mental states, cause them to do so. If that's true for them at time T, then by hypothesis it's true for the "god" agents as well.
It may be that, in the sense you have in mind, the protagonists simply do not have choice.
