  In a recent paper (Phys. Rev. D 94, 125016 (2016)), the authors argued that
the singularities of the two-point functions on the Poincar\'e domain of the
$n$-dimensional anti-de Sitter spacetime ($\text{PAdS}_n$) have the Hadamard
form, regardless of which (Robin) boundary condition is chosen at the conformal
boundary. However, the argument used to prove this statement was based on an
incorrect expression for the two-point function $G^{+}(x,x')$, which was
obtained by demanding $\text{AdS}$ invariance for the vacuum state. In this
comment I show that their argument works only for Dirichlet and Neumann
boundary conditions and that the full $\text{AdS}$ symmetry cannot be respected
by nontrivial Robin conditions (i.e., those which are neither Dirichlet nor
Neumann). By studying the conformal scalar field on $\text{PAdS}_2$, I find the
correct expression for $G^{+}(x,x')$ and show that, notwithstanding this
problem, it still have the Hadamard form.
