The urge for higher resolution climate change scenarios has been widely recognized, particularly for conducting impact assessment studies. Statistical downscaling methods have shown to be very convenient for this task, mainly because of their lower computational requirements in comparison with nested limited-area regional models or very high resolution Atmosphere-ocean General Circulation Models. Nevertheless, although some of the limitations of statistical downscaling methods are widely known and have been discussed in the literature, in this paper it is argued that the current approach for statistical downscaling does not guard against misspecified statistical models and that the occurrence of spurious results is likely if the assumptions of the underlying probabilistic model are not satisfied. In this case, the physics included in climate change scenarios obtained by general circulation models, could be replaced by spatial patterns and magnitudes produced by statistically inadequate models. Illustrative examples are provided for monthly temperature for a region encompassing Mexico and part of the United States. It is found that the assumptions of the probabilistic models do not hold for about 70 % of the gridpoints, parameter instability and temporal dependence being the most common problems. As our examples reveal, automated statistical downscaling "black-box" models are to be considered as highly prone to produce misleading results. It is shown that the Probabilistic Reduction approach can be incorporated as a complete and internally consistent framework for securing the statistical adequacy of the downscaling models and for guiding the respecification process, in a way that prevents the lack of empirical validity that affects current methods.