The near-threshold behavior of the pp¯ invariant mass spectrum from the J/ψ→ωpp¯ decay reported recently by the BES Collaboration is analyzed. Our study demonstrates that there is indeed a clear enhancement in the pp¯ invariant mass spectrum near threshold as compared to the phase-space behavior. Moreover, this enhancement is nicely reproduced by the final state interaction in the relevant (S011) pp¯ partial wave as given by the Jülich nucleon–antinucleon model. Therefore, contrary to the statement by the BES Collaboration, their new data on J/ψ→ωpp¯ decay in fact strongly support the FSI interpretation of the pp¯ enhancement, seen also in other decay reactions.