Families of model "rugged landscape" potential energy functions have been constructed and examined, in order to clarify the molecular-level basis for the relationship between thermodynamic and kinetic behaviors of glassforming substances. The general approach starts by forming elementary basin units, each of which contains a single local minimum (inherent structure). These units are then spliced together to create a continuous composite potential with the requisite number of basins, upper and lower limits, and boundary conditions. We demonstrate by example that this approach creates wide topographic diversity. Specifically, many pairs of model potential functions exist that share identical thermodynamic properties (depth distribution of minima), but drastically different kinetics (overall topography). Thus, within the confines of this purely mathematical exercise, the "strong" versus "fragile" classifications of thermodynamics and of kinetics are logically disconnected. We conclude that the empirically-observed correlation between thermodynamic and kinetic behaviors embodied, for example, in the Adam-Gibbs equation, must rest upon an additional physical principle involving details of interparticle interactions, transcending the purely mathematical aspects of potential energy landscape topography.