  A delicate tension complicates the relationship between the topological
magnetoelectric effect (TME) in three-dimensional (3D) $\mathbb{Z}_2$
topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a
particular $\mathbb{Z}_2$ topological classification of the electronic ground
state of crystalline band insulators and the associated quantization of the
magnetoelectric response coefficient calculated using bulk linear response
theory but, according to standard symmetry arguments, simultaneously forbids a
nonzero magnetoelectric coefficient in any physical finite-size system. This
contrast between theories of magnetoelectric response in formal bulk models and
in real finite-sized materials originates from the distinct approaches required
to introduce notions of (electronic) polarization and orbital magnetization in
these fundamentally different environments. In this work we argue for a
modified interpretation of the bulk linear response calculations in
non-magnetic $\mathbb{Z}_2$ TIs that is more plainly consistent with TRS, and
use this interpretation to discuss the effect's observation - still absent over
a decade after its prediction. Motivated by analytical results, we conjecture a
type of microscopic bulk-boundary correspondence: a bulk insulator with
(generalized) TRS supports a magnetoelectric coefficient that is purely
itinerant (which is generically related to the geometry of the ground state) if
and only if magnetic surface dopants are required for the TME to manifest in
finite samples thereof. We conclude that in non-magnetic $\mathbb{Z}_2$ TIs the
TME is activated by magnetic surface dopants, that the charge density response
to a uniform dc magnetic field is localized at the surface and specified by the
configuration of those dopants, and that the TME is qualitatively less robust
against disorder than the integer quantum Hall effect.
