Aqueous suspensions of synthetic saponite clays have been studied using field-cycling NMR relaxometry. The saponite platelets form planar surfaces on which water molecules are adsorbed. As the strong-adsorption limit applies, "bulk mediated surface diffusion'' as originally suggested by Bychuk and O'Shaughnessy is expected to occur. That is, within the so-called retention time, adsorbate molecules tend to perform Levy walks along the surfaces. A corresponding formalism (the "pancake model'') is derived and compared with the experimental data. The low-frequency spin-lattice relaxation dispersion can perfectly be described on this basis. The platelet diameter can be estimated from the peculiar adsorbate dynamics on the surfaces in accordance with literature data.