  It is shown that the toy-model-based considerations of {\em loc. cit.} (see
also arXiv:1312.3395) are based on an incorrect, manifestly unphysical choice
of the Hilbert space of admissible quantum states. A two-parametric family of
all of the eligible correct and potentially physical Hilbert spaces of the
model is then constructed. The implications of this construction are discussed.
In particular, it is emphasized that contrary to the conclusions of {\em loc.
cit.} there is no reason to believe that the current form of the
$\mathcal{PT}$-symmetric quantum theory should be false as a fundamental
theory.
