We examine whether it is possible to derive the field strength distribution of quiet-Sun internetwork regions from very high spatial resolution polarimetric observations in the visible. In particular, we consider the case of the spectropolarimeter attached to the Solar Optical Telescope aboard Hinode. Radiative magnetoconvection simulations are used to synthesize the four Stokes profiles of the Fe I 630.2 nm lines. Once the profiles are degraded to a spatial resolution of 0.32" and added noise, we infer the atmospheric parameters by means of Milne-Eddington inversions. The comparison of the derived values with the real ones indicates that the visible lines yield correct internetwork field strengths and magnetic fluxes, with uncertainties smaller than ~150 G, when a stray-light contamination factor is included in the inversion. Contrary to the results of ground-based observations at 1", weak fields are retrieved wherever the field is weak in the simulation.