We have re-analysed the Ginga 2-18 keV X-ray observations of Seyfert 2 galaxies, and find that their mean spectrum can be described by a power law of index alpha~1, reflection from an optically thick accretion disc and/or molecular torus, and absorption from cold material. These objects then have a mean intrinsic spectrum similar to that of Seyfert 1s, and so support the predictions of orientation-dependent Seyfert unification schemes. There is also an intrinsic dispersion about this mean spectrum which is similar to that seen in the Seyfert 1s. We demonstrate this dispersion explicitly in several objects with data of high signal-to-noise ratio, where the intrinsic spectra are much flatter or steeper than alpha~1 despite the inclusion of neutral reflection, ionized reflection, unobscured reflection and/or ionized absorption. This is important, as a currently popular explanation for the Seyfert 1 spectra (and hence the Seyfert 2 spectra presented here) is that of Haardt & Maraschi, in which the UV seed photons for Compton cooling of the energetic electrons are produced from reprocessing of the hard X-ray spectrum in an accretion disc. This feedback model correctly predicts the observed mean spectral index of alpha~1 for a wide range of optical depths. Steeper spectra than this can be produced naturally in these models if the thermal plasma optical depth approaches unity or if there is intrinsic emission from the disc itself. However, such models are unable easily to explain intrinsic spectra much flatter than alpha~1. Thus the flat-spectrum sources presented here, which are most reminiscent of the atypical Seyfert galaxy NGC 4151, pose serious problems for the Haardt & Maraschi model if there are no other external processes modifying the hard X-ray spectra in Seyfert galaxies.