If this is the case the statistics seem to be on the side of being in one rather than not.

This is what people are missing, and this is the core of the argument. While it's true that we have no empirical reason to think we're in a simulation, the argument doesn't appeal to empirical evidence.

The argument relies on an automatic outcome of a couple of premises. Simulations with conscious inhabitants are either possible, or impossible. So, for the sake of argument, assume we grant that they're possible, and that any civilization that runs them is more likely to run more than one than only one.

If these two premises are true, then there would be more simulated universes with observers than "real" universes with observes. So if there are more simulated universes with conscious observes than there are "real" universes with conscious observers, then a randomly chosen observer would more than likely find himself in a simulated universe. We're stuck with that conclusion, unless we want to go back and revoke our acceptance of the premises.

So it comes down to whether or not simulations sophisticated enough to have conscious observers is possible. Whether we see evidence that we ourselves are in a simulation is a secondary issue. I'd also argue that it doesn't matter if we're in a simulation, but that's a separate argument.