In the collision He+ + He-->He+ + He*, excitation at low incident ion energies (<~ 1 keV) proceeds via a pseudocrossing of the elastic 2Σg diabatic potential with excited-state 2Σg potentials. As previously reported, this excitation mechanism fails to explain diverse experimental data concerning total excitation cross sections. A new physical mechanism is hypothesized, its existence verified, and it is shown to provide good qualitative and semiquantitative interpretation of the observations. Nonadiabatic couplings among some excited states occur at pseudocrossings of the respective inelastic-channel molecular potentials at large internuclear separations, resulting in coherent phase interference in the inelastic-scattering amplitudes. A linear-combination-of-atomic-orbitals (LCAO) calculation of 18 excited-state 2Σg potentials of the intermediate (He2+)* system verifies the presence of these outer pseudocrossing. Such a mechanism is shown to be likely in many ion-atom collisions.