Although your overall point is correct, I disagree with this statement. It is in fact only theory that distinguishes between continuous systems and very high resolution discrete ones, because the time-evolution of an ideal computer is nowhere differentiable while the time-evolution of a physical system is everywhere differentiable.
Indeed, it is not only "discrete" and "continuous" that are indistinguishable below a certain threshold. For any data, there are an infinite number of continuous theories that are all indistinguishable from each other, and also are indistinguishable from an infinite number of discrete theories, which are yet also indistinguishable from each other - all that it takes for this to happen is for us to agree that the data doesn't specify anything below a certain scale. Then, every theory that agrees on the large scale will match the data, leaving room for anything you can imagine at the bottom. So discrete vs. continuous isn't the core point.