The nanostructure of materials is supposed to affect polymer adhesion at the solid/liquid interface by variations of the exposed surface area. In contrast, our studies on the nanotribology of single recombinant spider silk proteins onto smooth and rough surfaces made of surgical stainless steel show no effect of the surface morphology. This is explained by the velocity dependence of the desorption process, which reveals a negligible friction and a high in-plane mobility at the molecular scale. We compare our results to all atomistic molecular dynamics simulations that allow estimating an upper limit for the molecular friction coefficient.