The recent measurements by the BES Collaboration of J/psi decays into a photon and a proton-antiproton pair indicate a strong enhancement at the proton-antiproton threshold not observed in the decays into a neutral pion and a proton-antiproton pair. Is this enhancement due to a proton-antiproton quasi-bound state or a baryonium? A natural explanation follows from a traditional model of proton-antiproton interactions based on G-parity transformation. The observed proton-antiproton structure is due to a strong attraction in the 1S0 state, and possibly to a near-threshold quasi-bound state in the 11S0 wave.