It is shown that broad-line region (BLR) line profiles ranging from the classic "logarithmic" profile to double-peaked, disk-like profiles are readily explained by the distribution of BLR gas proposed by Gaskell, Klimek, & Nazarova (2007; GKN) without any need to invoke fundamental differences in the AGNs other than differing viewing angles. It is argued that the highly-variable thermal energy generation in AGNs originates off axis in regions that cannot be axially symmetric. This off-axis model readily explains the varying degrees of temporal correlation found in multi-wavelength variability studies, the strong, variable asymmetry of BLR line profiles, the varying time delays in the response of the BLR to different continuum events, how narrow velocity ranges of line profiles will often appear to respond differently or not at all to continuum variability, complex changes in the Balmer decrement with velocity, inconsistent and variable inflow/outflow signatures found in velocity-resolved reverberation mapping, the diversity of velocity-dependent polarizations observed, and polarization variability. The fundamentally non-axisymmetric nature of AGN continuum variability severely limits what can be learned from reverberation mapping. In particular, high-fidelity reverberation mapping is not possible. There will be systematic orientation-dependent errors in black hole mass determinations. The effects of off-axis emission will mask subtle signatures of possible close supermassive black hole binaries. Some tests of the off-axis-variability model are proposed.