I like your take on it. Unless the entities running the simulator directly enter the simulation and tell / show everyone that it is a simulation, we'll never know - and it won't actually matter.
That said, it does make sense; do characters in The Sims as it is now, or as it may be in a hundred, a thousand, ten thousand years, know that they're living in a simulation? We're adding more and more computing power, and more and more details to our own simulations; at the current pace it seems to be a matter of time before we can simulate physics to the smallest quantum details, at an universal scale, at a fraction of the energy cost of our own universe. And maybe not real-time, but if we live in a simulation, who is to say that time as we experience it ourselves passes as fast on the "outside"? It could be that every second of our existence takes the equivalent of a hundred years outside of the simulation. But we're going down a philosophical rabbithole now.