Abstract A large fraction of gamma-ray burst (GRB) spectra are very hard below the peak. Indeed, the observed distribution of sub-peak power-law indices, α, has been used as an argument for a photospheric origin of GRB spectra. Here, we investigate what fraction of GRBs have spectra that are consistent with emission from a photopshere in a non-dissipative outflow. This is the simplest possible photospheric emission scenario. We create synthetic spectra, with a range of peak energies, by folding the theoretical predictions through the detector response of the FERMI/GBM detector. These simulated spectral data are fitted with typically employed empirical models. We find that the low-energy photon indices obtain values ranging −0.4 < α < 0.0, peaking at around −0.1, thus covering a non-negligible fraction of observed values. These values are significantly softer than the asymptotic value of the theoretical spectrum of α ∼ 0.4. The reason for the α values to be much softer than expected, is the limitation of the empirical functions to capture the true curvature of the theoretical spectrum. We conclude that more than a quarter of the bursts in the GBM catalogue have at least one time-resolved spectrum, whose α values are consistent with spectra from a non-dissipative outflow, releasing its thermal energy at the photosphere. The fraction of spectra consistent with emission from the photosphere will increase even more if dissipation of kinetic energy in the flow occurs below the photosphere.