We report results of lattice Boltzmann simulations of a high-speed drainage of liquid films squeezed between a smooth sphere and a randomly rough plane. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. However, this force reduction does not represent slippage. The computed force is exactly the same as that between equivalent smooth surfaces obeying no-slip boundary conditions, but located at an intermediate position between peaks and valleys of asperities. The shift in hydrodynamic thickness is shown to depend on the height and density of roughness elements. Our results do not support some previous experimental conclusions on a very large and shear-dependent boundary slip for similar systems.