  It is widely reported, based on clustering measurements of observed active
galactic nuclei (AGN) samples, that AGN reside in similar mass host dark matter
halos across the bulk of cosmic time, with log $M/M_\odot$~12.5-13.0 to z~2.5.
We show that this is due in part to the AGN fraction in galaxies rising with
increasing stellar mass, combined with AGN observational selection effects that
exacerbate this trend. Here, we use AGN specific accretion rate distribution
functions determined as a function of stellar mass and redshift for
star-forming and quiescent galaxies separately, combined with the latest
galaxy-halo connection models, to determine the parent and sub-halo mass
distribution function of AGN to various observational limits. We find that
while the median (sub-)halo mass of AGN, $\approx10^{12}M_\odot$, is fairly
constant with luminosity, specific accretion rate, and redshift, the full halo
mass distribution function is broad, spanning several orders of magnitude. We
show that widely used methods to infer a typical dark matter halo mass based on
an observed AGN clustering amplitude can result in biased, systematically high
host halo masses. While the AGN satellite fraction rises with increasing parent
halo mass, we find that the central galaxy is often not an AGN. Our results
elucidate the physical causes for the apparent uniformity of AGN host halos
across cosmic time and underscore the importance of accounting for AGN
selection biases when interpreting observational AGN clustering results. We
further show that AGN clustering is most easily interpreted in terms of the
relative bias to galaxy samples, not from absolute bias measurements alone.
