  Velocity-resolved reverberation mapping suggests that the broad-line regions
(BLRs) of AGNs can have significant net inflow. We use the STOKES radiative
transfer code to show that electron and Rayleigh scattering off the BLR and
torus naturally explains the blueshifted profiles of high-ionization lines and
the ionization dependence of the blueshifts. This result is insensitive to the
geometry of the scattering region. If correct, this model resolves the
long-standing conflict between the absence of outflow implied by
velocity-resolved reverberation mapping and the need for outflow if the
blueshifting is the result of obscuration. The accretion rate implied by the
inflow is sufficient to power the AGN. We suggest that the BLR is part of the
outer accretion disk and that similar MHD processes are operating. In the
scattering model the blueshifting is proportional to the accretion rate so
high-accretion-rate AGNs will show greater high-ionization line blueshifts as
is observed. Scattering can lead to systematically too high black hole mass
estimates from the C IV line. We note many similarities between narrow-line
region (NLR) and BLR blueshiftings, and suggest that NLR blueshiftings have a
similar explanation. Our model explains the higher blueshifts of broad
absorption line QSOs if they are more highly inclined. Rayleigh scattering from
the BLR and torus could be more important in the UV than electron scattering
for predominantly neutral material around AGNs. The importance of Rayleigh
scattering versus electron scattering can be assessed by comparing line
profiles at different wavelengths arising from the same emission-line region.
