Recently, Kallivayalil et al. derived new values of the proper motion for the Large and Small Magellanic Clouds (LMC and SMC, respectively). The spatial velocities of both Clouds are unexpectedly higher than their previous values resulting from agreement between the available theoretical models of the Magellanic System and the observations of neutral hydrogen (H I) associated with the LMC and the SMC. Such proper motion estimates are likely to be at odds with the scenarios for creation of the large-scale structures in the Magellanic System suggested so far. We investigated this hypothesis for the pure tidal models, as they were the first ones devised to explain the evolution of the Magellanic System, and the tidal stripping is intrinsically involved in every model assuming the gravitational interaction. The parameter space for the Milky Way (MW)-LMC-SMC interaction was analyzed by a robust search algorithm (genetic algorithm) combined with a fast, restricted N-body model of the interaction. Our method extended the known variety of evolutionary scenarios satisfying the observed kinematics and morphology of the Magellanic large-scale structures. Nevertheless, assuming the tidal interaction, no satisfactory reproduction of the H I data available for the Magellanic Clouds was achieved with the new proper motions. We conclude that for the proper motion data by Kallivayalil et al., within their 1? errors, the dynamical evolution of the Magellanic System with the currently accepted total mass of the MW cannot be explained in the framework of pure tidal models. The optimal value for the western component of the LMC proper motion was found to be ?W lmcgsim -1.3 mas yr-1 in case of tidal models. It corresponds to the reduction of the Kallivayalil et al. value for ?W lmc by ? 40% in its magnitude.