In this third paper of the series we present our interpretation for the rise in the degree of polarization across the broad wings of Hβ and Hα compared with the nonstellar continuum that is observed in all galaxies in our sample but NGC 1068 (Paper Ⅱ). The similarity of polarization angles between the broad-line wings and adjacent continuum, and their perpendicular relationship with the radio and/or extended emission structure axis strongly suggest that the obscuring torus picture with the general scattering geometry proposed for NGC 1068 is basically correct. If so, the observed polarizations can be explained by the hypothesis that, in addition to the scattered (hence polarized) continuum radiation from the obscured nucleus, there exists a substantial unpolarized continuum underlying and accounting for ～ 60%-90% of the total featureless continua of these Seyfert 2 galaxies. The continuum polarizations after the removal of this diluting component are generally very high (approx >15%), and in good accord with those expected from the obscuring torus/scattering electron models. Available evidence also suggests that this unpolarized continuum may represent the optically thin thermal radiation from the scattering region itself. Polarized broad lines appear to be found predominately in multiple perhaps interacting systems of galaxies. Barring strong selection effects, this may indicate that perturbing or merging processes play an important role in the existence and/or detection of hidden broad-line regions in Seyfert 2 galaxies at some stages of their evolution.
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