We present a simulation and modeling study of electro-osmotic flow of an aqueous cesium chloride solution confined in a charged amorphous silica slot. Contrasting traditional models of the electric double layer, molecular dynamics simulations indicate that there is no stagnant layer, no Stern layer conduction, and no outer Helmholtz layer. The description of the interface requires two considerations. First, a distinction has to be made between free and surface-bonded ions. The latter do not form a physical layer but rather a set of ion-surface contact pairs. Second, the mobility of the free ions is reduced relative to their bulk value. This hydrodynamic effect needs to be included. These two concepts, coupled to simple macroscopic equations, are sufficient to describe surface conductivity and electro-osmotic flow in the frame of classical mean-field treatment. We show that surface conduction is negative at high concentration, and the Bikerman formula is only valid at low concentration.