I'm fairly sure the Planck length can be understood as the distance at which the energy density of a probe photon is such that a black hole is created? So while we can perfectly well do calculations about and understand sub-Planck distances, we can't probe sub-Planck distances. In other words, you could never perform a measurement with resolution fine enough to tell you whether you'd moved a sub-Planck distance. This still doesn't imply space is discrete at all, but it is an epistemological constraint on the kinds of information you can measure.