A model proposed by Rioux to explain Hund's rule is investigated. Although the largest contribution to the singlet-triplet splitting in the two-electron atomic systems is the nuclear attraction term, this arises from different optimum scale factors in the two states and that difference is driven by the electron-electron exchange term. The incorrect prediction that the singlet energy is lower for the He 1s2s states is a consequence of the fact that in the model used by Rioux the singlet-state wave function is not orthogonal to the ground-state wave function, as it must be for a variational calculation. (Contains 1 figure and 1 table.)