  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,
$\alpha$, 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 fit with typically employed empirical models. We find that
the low-energy photon indices obtain values ranging $-0.4 < \alpha < 0.0$,
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 $\alpha \sim 0.4$. The reason for the $\alpha$-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 $1/4$ of the bursts in the GBM catalogue have at least one
time-resolved spectrum, whose $\alpha$-values are consistent with 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.
