We address the antireflection (AR) properties of periodic surfaces, or metasurfaces, supporting substrate waves. The work is motivated by recent literature where AR bands formed by substrate-wave propagation are incorrectly attributed to Mie scattering. In contrast, as clearly shown here, substrate-wave generation with corresponding AR signatures is a diffractive effect due to a periodic lattice and is not due to particle scattering as in Mie resonance. Treating both 1D and 2D surfaces, we demonstrate a clear quantitative connection between major AR loci and corresponding total substrate transmittance loci via maps in period versus wavelength. As shown, this holds for fully dispersed, lossy surfaces as well. The results presented here serve to elucidate the physical properties of periodic metasurfaces placed on substrates admitting propagating diffraction orders and may inform the design and implementation of grating-based AR structures.