Continuum models of flexible polymers give physically incorrect results in situations where polymers are "localized" to restricted regions of space. Limitations of continuum chain theories for confined polymers are illustrated for surface-interacting polymers where both lattice and continuum calculations can be performed exactly for ideal chains. This comparison reveals the details of the breakdown of the continuum chain model in the regime of strong polymer adsorption. As a remedy to this difficulty, we formally introduce a corrected continuum chain theory by taking the spatial dimension d to depend on the surface interaction in such a way that the lattice and continuum model calculations are required to be consistent for weak and strong polymer adsorption.