Unless P=NP, I don't think it's obvious that such a simulation could be built to be perfectly (to the limits of human science) indistinguishable from the original system being simulated. There are a lot of results which are easy to verify but arbitrarily hard to compute, and we encounter plenty of them in nature and physics. I suppose the simulators could be futzing with our brains to make us think we were verifying incorrect results, but now we're alarmingly close to solipsism again.

I guess one way to to test this hypothesis would be to try to construct a system with easy-to-verify but arbitrarily-hard-to-compute behavior ("Project: Piss Off God"), and then scrupulously observe its behavior. Then we could keep making it more expensive until we got to a system that really shouldn't be practically computable in our universe. If nothing interesting happens, then we have evidence that either we aren't in a simulation, or P=NP.