  Theories of $f(T)$ gravity are being actively confronted with cosmological
observations, and are being studied for their potential to solve famous
problems of cosmology. A necessary step is to extend these studies to
astrophysical settings. However, to this end one must understand the structure
of spherically symmetric solutions. We show that two different known approaches
to these solutions are actually fully equivalent from the point of view of
Lorentz-covariant formalism. Moreover, we explain Bianchi identities in $f(T)$
gravity and apply them to show that the corresponding equations are always
compatible. It puts these efforts on much firmer grounds than before.
