The other answer is that we are living in a much grainier simulation, and either there are super-intelligent demons flitting around between ticks of the world clock, falsifying the results of physics experiments and making smoke detectors work, or that there is a global conspiracy of some kind, orchestrated by the simulators, to which most of science is party, to convince the bulk of the population that we are living in a more computationally expensive universe.
To the extent that super-intelligent demons / global conspiracies are both required for a grainier simulation to work and unreasonable to include in a simulation hypothesis, this undermines your claim that "We could easily be supplied with a far, far grainier simulation and never know the difference. If you're interested in humans, you'd certainly take running many orders of magnitude more simulations, over running a single, imperceptibly more accurate simulation, far slower."
Not for the simulations to work - only for the simulations to look exactly like the universe we now find ourselves in. 95% of human history could have played out, unchanged, in a universe without relativistic effects or quantum weirdness, far more inexpensively. We simply wouldn't have had the tools to measure the difference.
Even after the advent of things like particle accelerators, we could still be living in a very similar but-less-expensive universe, and things would be mostly unchanged. Our experiments would tell us that Newtonian mechanics are per...
Jonathan Birch recently published an interesting critique of Bostrom's simulation argument. Here's the abstract:
The paper is behind a paywall, but I have uploaded it to my shared Dropbox folder, here.
EDIT: I emailed the author and am glad to see that he's decided to participate in the discussion below.