  The Galactic Center Excess (GCE) in GeV gamma rays has been debated for over
a decade, with the possibility that it might be due to dark matter annihilation
or undetected point sources such as millisecond pulsars (MSPs). This study
investigates how the gamma-ray emission model ($\gamma$EM) used in Galactic
center analyses affects the interpretation of the GCE's nature. To address this
issue, we construct an ultra-fast and powerful inference pipeline based on
convolutional Deep Ensemble Networks. We explore the two main competing
hypotheses for the GCE using a set of $\gamma$EMs with increasing parametric
freedom. We calculate the fractional contribution ($f_{\mathrm{src}}$) of a dim
population of MSPs to the total luminosity of the GCE and analyze its
dependence on the complexity of the $\gamma$EM. For the simplest $\gamma$EM, we
obtain $f_{\mathrm{src}} = 0.10 \pm 0.07$, while the most complex model yields
$f_{\mathrm{src}} = 0.79 \pm 0.24.$ In conclusion, we find that the statement
about the nature of the GCE (dark matter or not) strongly depends on the
assumed $\gamma$EM. The quoted results for $f_{\mathrm{src}}$ do not account
for the additional uncertainty arising from the fact that the observed
gamma-ray sky is out-of-distribution concerning the investigated $\gamma$EM
iterations. We quantify the reality gap between our $\gamma$EMs using
deep-learning-based One-Class Deep Support Vector Data Description networks,
revealing that all employed $\gamma$EMs have gaps to reality. Our study casts
doubt on the validity of previous conclusions regarding the GCE and dark
matter, and underscores the urgent need to account for the reality gap and
consider previously overlooked ''out of domain'' uncertainties in future
interpretations.
