  The IceCube Neutrino Observatory at the South Pole has measured astrophysical
neutrinos using through-going and starting events in the TeV to PeV energy
range. The origin of these astrophysical neutrinos is still largely unresolved,
and among their potential sources could be dark matter decay. Measurements of
the astrophysical flux using muon neutrinos are in slight tension with starting
event measurements. This tension is driven by an excess observed in the energy
range of 40-200 TeV with respect to the through-going expectation. Previous
works have considered the possibility that this excess may be due to heavy dark
matter decay and have placed constraints using gamma-ray and neutrino data.
However, these constraints are not without caveats since they rely on the
modeling of the astrophysical neutrino flux and the sources of gamma-ray
emission. In this work, we derive background-agnostic galactic and
extragalactic constraints on decaying dark matter by considering Tibet
AS$_\gamma$ data, Fermi-LAT diffuse data, and the IceCube high-energy starting
event sample. For the gamma-ray limits, we investigate the uncertainties on
secondary emission from electromagnetic cascades during propagation arising
from the unknown intensity of the extragalactic background light. We find that
such uncertainties amount to a variation of up to $\sim 55\%$ in the gamma-ray
limits derived with extragalactic data. Our results imply that a significant
fraction of the astrophysical neutrino flux could be due to dark matter and
that ruling it out depends on the assumptions on the gamma-ray and neutrino
background. The latter depends on the yet unidentified sources.
