  We investigate in-gap states emerging when a single $3d$ transition metal
impurity is embedded in topological insulators (Bi$_2$Te$_3$ and Bi$_2$Se$_3$).
We use a combined approach relying on first-principles calculations and an
Anderson impurity model. By computing the local density of states of Cr, Mn, Fe
and Co embedded not only in surfaces of Bi$_2$Te$_3$ and of Bi$_2$Se$_3$ but
also in their bulk phases, we demonstrate that in-gap states originate from the
hybridization of the electronic states of the impurity with bulk bands and not
with the topological surface states as it is usually assumed. This finding is
analyzed using a simplified Anderson impurity model. These observations are in
contradiction with the prevailing models used to investigate the magnetic
doping of topological insulators [R. R. Biswas et al. PRB 81, 233405 (2010), A.
M. Black-Schafer et al. PRB 91, 201411 (2015)], which attribute the origin of
the in-gap states to the hybridization with the topological surface states.
