A new interpretation of the spherically-symmetric pair potential derived by inversion of the thermophysical properties for non-spherically symmetric molecular systems is presented. The interpretation is based on the original inversion equations cast in a form that makes the connection of the potential from inversion to the full anisotropic potential clearer. Tests on potential models confirm the usefulness of the new formulation because, at least for two simple models, the link between the full potential and the potential from inversion is particularly straightforward.