  Primordial black holes (PBHs) are convenient candidates to explain the
elusive dark matter (DM). However, years of constraints from various
astronomical observations have constrained their abundance over a wide range of
masses, leaving only a narrow window open at $10^{17}\,{\rm g} \lesssim M
\lesssim 10^{22}\,$g for all DM in the form of PBHs. We reexamine this disputed
window with a critical eye, interrogating the general hypotheses underlying the
direct photon constraints. We review 4 levels of assumptions: i) instrument
characteristics, ii) prediction of the (extra)galactic photon flux, iii)
statistical method of signal-to-data comparison and iv) computation of the
Hawking radiation rate. Thanks to Isatis, a new tool designed for the public
Hawking radiation code BlackHawk, we first revisit the existing and prospective
constraints on the PBH abundance and investigate the impact of assumptions
i)-iv). We show that the constraints can vary by several orders of magnitude,
advocating the necessity of a reduction of the theoretical sources of
uncertainties. Second, we consider an "ideal" instrument and we demonstrate
that the PBH DM scenario can only be constrained by the direct photon Hawking
radiation phenomenon below $M_{\rm max} \sim 10^{20}\,$g. The upper part of the
mass window should therefore be closed by other means.
