Context. The ESA/Rosetta mission has been orbiting comet 67P/Churyumov-Gerasimenko since August 2014, measuring its dayside plasma environment. The ion spectrometer onboard Rosetta has detected two ion populations, one energetic with a solar wind origin (H+, He2+, He+), the other at lower energies with a cometary origin (water group ions such as H2O+). He+ ions arise mainly from charge-exchange between solar wind alpha particles and cometary neutrals such as H2O. Aims. The He+ and He2+ ion fluxes measured by the Rosetta Plasma Consortium Ion Composition Analyser (RPC-ICA) give insight into the composition of the dayside neutral coma, into the importance of charge-exchange processes between the solar wind and cometary neutrals, and into the way these evolve when the comet draws closer to the Sun. Methods. We combine observations by the ion spectrometer RPC-ICA onboard Rosetta with calculations from an analytical model based on a collisionless neutral Haser atmosphere and nearly undisturbed solar wind conditions. Results. Equivalent neutral outgassing rates Q can be derived using the observed RPC-ICA He+/He2+ particle flux ratios as input into the analytical model in inverse mode. A revised dependence of Q on heliocentric distance Rh in AU is found to be Rh -7.06Rh-7.06 between 1.8 and 3.3 AU, suggesting that the activity in 2015 differed from that of the 2008 perihelion passage. Conversely, using an outgassing rate determined from optical remote sensing measurements from Earth, the forward analytical model results are in relatively good agreement with the measured RPC-ICA flux ratios. Modelled ratios in a 2D spherically-symmetric plane are also presented, showing that charge exchange is most efficient with solar wind protons. Detailed cometocentric profiles of these ratios are also presented. Conclusions. In conclusion, we show that, with the help of a simple analytical model of charge-exchange processes, a mass-capable ion spectrometer such as RPC-ICA can be used as a "remote-sensing" instrument for the neutral cometary atmosphere. © 2016 ESO.