We investigate the influence of spatial dispersion on atom-surface quantum friction. We show that for atom-surface separations shorter than the carrier's mean free path within the material, the frictional force can be several orders of magnitude larger than that predicted by local optics. In addition, when taking into account spatial dispersion effects, we show that the commonly used local thermal equilibrium approximation underestimates by approximately 95% the drag force, obtained by employing the recently reported nonequilibrium fluctuation-dissipation relation for quantum friction. Unlike the treatment based on local optics, spatial dispersion in conjunction with corrections to local thermal equilibrium not only change the magnitude but also the distance scaling of quantum friction. ; Comment: 10 pages, 1 figure