We inspect the first-order electron-electron capture scenario for transfer ionization that has been recently formulated by Voitkiv et al. (Phys. Rev. A 86, 012709 (2012) and references therein). Using the multichannel scattering theory for many-body
systems with Coulomb interactions, we show that this scenario is just a part of the well-studied Oppenheimer-Brinkmann-Kramers approximation. Accurate numerical calculations in this approximation for the proton-helium transfer ionization reaction exhibit no appreciable manifestation of the claimed mechanism.
