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 perfectly correct to as many decimal places as we can measure, and that atoms are distinct, discrete point objects with a well-defined mass, position, and velocity, and that would be fine. That'd just be the way things are. Very few non-physicist people would be strongly impacted by the change.
In other words, if they're interested in simulating humans, there are very simple approximations that would save an enormous quantity of computing power per second. The fact that we don't see those approximations in place (and, in fact, are living in such a computationally lavish universe) is evidence that we are not living in a simulation.
This argument is anthropomorphizing. It assumes that the purpose of the purported simulation is to model humanity. Suppose it isn't? Suppose the purpose of the simulation is to model a universe with certain physical laws, and one of the unexpected outcomes is that intelligent technological life happens to evolve on a small rocky planet around one star out in the spiral arm of one galaxy. That could be a completely unexpected outcome, maybe even an unnoticed outcome, of a simulation with a very different purpose.
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.