Long-range electrostatic attractions between identical colloidal particles in confined geometries have been observed experimentally by many workers. A satisfactory theoretical explanation for this behavior has proven elusive. Recent numerical calculations and reports (Nature 393, 621-623, 663-665 (1998)), however, have suggested that this problem is closed by demonstrating that this surprising effect is to be found naturally within the well-established Poisson-Boltzmann (PB) theory. We rigorously prove that these claims are false; within the framework of the PB theory, the interaction between identical colloidal particles is always repulsive, irrespective of whether the particles are isolated or confined. A satisfactory theoretical explanation of this surprising phenomenon thus remains an unresolved problem,