It is known that, at optical frequencies, a simple interface between a perfect dielectric and a real metal can sustain the propagation of surface plasmon polaritons only for P-polarized electromagnetic waves, being S-polarized surface plasmons are prohibited. In this work, we formally show that, strictly speaking, both polarization states are in fact prohibited and that only P-polarized pseudosurface waves are allowed, which is what is encountered in the applications. The existence of such pseudosurface modes allows one to reconcile theory and experimental evidence, but also sets limits for them to be considered as modes bound to the interface.