An excess of gamma rays at GeV energies has been pointed out in the Fermi-LAT data. This signal comes from a narrow region centred around the Galactic center and has been interpreted as possible evidence for light dark matter particles annihilating either into a mixture of leptons-anti leptons and b-bbar or into b-bbar only. Focussing on the prompt gamma-ray emission, previous works found that the best fit to the data corresponds to annihilations proceeding predominantly into b-bbar. However, here we show that omitting the diffuse photon emission originating from primary and secondary electrons produced in dark matter annihilations can actually lead to the wrong conclusion. Accounting for this emission, we find that not only are annihilations of ~ 10 GeV particles into a purely leptonic final state allowed, but such annihilations actually provide a better fit than the pure b-bbar channel. We conclude our work with a possible test of these leptophilic scenarios based on the spectral feature of the gamma-ray emission at lower energies and larger latitude.