That's not actually true, or at least it is not currently known. It is very well possible that distances less than a Planck length have meaning, or maybe distances lose all meaning a couple of orders of magnitude above the Planck length. We just don't know the physical laws at that scales.

If you consider at what energy a photon (E = hc/λ) will be able to resolve, i.e. have a wavelength equal to, the Schwarzschild radius of that energy (r = 2GM/c² with E = mc²), then you get the Planck length up to a factor of root two [1], implying that measuring a Planck distance requires a photon so energetic that it turns that region into a black hole. If, very big if, the known laws still apply at those scales.

[1] To get the Planck length, the wavelength must be doubled, i.e. be equal to the diameter instead of the Schwarzschild radius.

  r = 2GM/c²  →  m = rc²/2G  →  E = rc⁴/2G (with E = mc²)

  hc/λ = rc⁴/2G → hc/2r = rc⁴/2G (with λ = 2r) → r² = hG/c³ → lₚ = r = √hG/c³