In fitting an ab initio potential for H2O-H-2, Phillips et al. [J. Chem. Phys. 101, 5824 (1994)] excluded certain terms in the angular expansion they believed to vanish because of "the requirement that the potential is invariant to inversion of all coordinates through the origin." However, there has been some question in the literature as to whether these terms must, in fact, vanish owing to spatial inversion symmetry. By providing counterexamples, it is demonstrated here that this is not required by fundamental spatial symmetry. However, these terms do appear to vanish for realistic molecular interactions and this symmetry may arise from the two-body nature of the electrostatic Hamiltonian.