The wet-oxidation of a single crystal Cu(111) foil is studied by growing single crystal graphene islands on it followed by soaking it in water. O-18-labeled water is also used; the oxygen atoms in the formed copper oxides in both the bare and graphene-coated Cu regions come from water. The oxidation of the graphene-coated Cu regions is enabled by water diffusing from the edges of graphene along the bunched Cu steps, and along some graphene ripples where such are present. This interfacial diffusion of water can occur because of the separation between the graphene and the "step corner" of bunched Cu steps. Density functional theory simulations suggest that adsorption of water in this gap is thermodynamically stable; the "step-induced-diffusion model" also applies to graphene-coated Cu surfaces of various other crystal orientations. Since bunched Cu steps and graphene ripples are diffusion pathways for water, ripple-free graphene is prepared on ultrasmooth Cu(111) surfaces and it is found that the graphene completely shields the underlying Cu from wet-oxidation. This study greatly deepens the understanding of how a graphene-coated copper surface is oxidized, and shows that graphene completely prevents the oxidation when that surface is ultrasmooth and when the graphene has no ripples or wrinkles.