The approximation is the belief that things can happen simultaneously. It is approximating along the fact that we only need to concern ourselves with a single reference frame.

I think the difference in the scenario you proposed is that we can conceive of a practical situation in which someone on Pluto sends a message and waits for a reply. We can then say that they are going to have to wait at least 10 hours to receive a reply. This has meaning.

But when the distances become too great the urge is to resist believing that things have an existence beyond the interactions of particles. There is no practical reality to that object beyond our ability to observe it when the light reaches us.