In this third paper of the series we present our interpretation for th
e rise in the degree of polarization across the broad wings of H beta
and H alpha 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 continu
um, and their perpendicular relationship with the radio and/or extende
d emission structure axis strongly suggest that the obscuring torus pi
cture with the general scattering geometry proposed for NGC 1068 is ba
sically correct. If so, the observed polarizations can be explained by
the hypothesis that, in addition to the scattered (hence polarized) c
ontinuum radiation from the obscured nucleus, there exists a substanti
al unpolarized continuum underlying and accounting for similar to 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 (greater than or similar to 15%), and in good
accord with those expected from the obscuring torus/scattering electro
n models. Available evidence also suggests that this unpolarized conti
nuum may represent the optically thin thermal radiation from the scatt
ering region itself. Polarized broad lines appear to be found predomin
ately in multiple perhaps interacting systems of galaxies. Barring str
ong selection effects, this may indicate that perturbing or merging pr
ocesses play an important role in the existence and/or detection of hi
dden broad-line regions in Seyfert 2 galaxies at some stages of their
evolution.