Recent measurements of the scattering of He and Ne atoms at Rh(110) suggest that these two rare-gas atoms measure a qualitatively different surface corrugation: While Ne atom scattering seemingly reflects the electron-density undulation of the substrate surface, the scattering potential of He atoms appears to be anticorrugated. An understanding of this perplexing result is lacking. In this paper we present density functional theory calculations of the interaction potentials of He and Ne with Rh(110). We find that, and explain why, the nature of the interaction of the two probe particles is qualitatively different, which implies that the topographies of their scattering potentials are indeed anticorrugated.