  Asteroseismology can provide joint constraints on masses and radii of
individual stars. While this approach has been extensively tested for red giant
branch (RGB) stars, it has been more difficult to test for helium core-burning
red-clump (RC) giants because of the lack of fundamental calibrators. To
provide independent mass estimates, we utilize a number of widely used
horizontal-branch (HB) models in the literature, and derive photometric masses
from a comparison with $griBVI_CJHK_s$ photometry. Our selected models disagree
with each other on the predicted mass-luminosity-temperature relation. We adopt
first-order corrections on colors and magnitudes to minimize the dispersion
between different models by forcing models to match the observed location in
the solar-metallicity cluster M67. Even for these calibrated models, however,
the internal consistency between models deteriorates at higher metallicities,
and photometric masses become smaller than asteroseismic masses, as seen from
metal-rich field RC stars with Gaia parallaxes. Similarly, the average
photometric mass for metal-rich NGC 6791 stars ranges from $0.7\ M_\odot$ to
$1.1\ M_\odot$, depending on the specific set of models employed. An ensemble
average of the photometric masses ($0.88\pm0.16\ M_\odot$) in NGC 6791 is
marginally consistent with the asteroseismic mass ($1.16\pm0.04\ M_\odot$).
There is a clear tension between the masses that one would predict from
photometry for metal-rich field RC stars, asteroseismic masses, and those that
would be expected from the ages of stars in the Galactic disk populations and
canonical RGB mass loss. We conclude that standard RC models need to be
re-examined in light of these powerful new data sets.
