We simply do not have enough information on the nature of reality to decide who is right here.

If space-time does turn out the be physically discrete at the planck length, and the limits of our measurements are actually reflecting the universe's true discontinuous nature, then this would imply that there would be a limit to how much state you could push into an atom.

Any real physicists please feel free to shoot me down in flames here. This is just my (plainly) limited understanding of the situation.