  We reconsider the phase diagram of a three-dimensional $\mathbb{Z}_2$
topological insulator in the presence of short-ranged potential disorder with
the insight that non-perturbative rare states destabilize the noninteracting
Dirac semimetal critical point separating different topological phases. Based
on our numerical data on the density of states, conductivity, and
wavefunctions, we argue that the putative Dirac semimetal line is destabilized
into a diffusive metal phase of finite extent due to non-perturbative effects
of rare regions. We discuss the implications of these results for past and
current experiments on doped topological insulators.
