  Two well studied dwarf galaxies -- NGC 3109 and NGC 6822 -- present some of
the strongest observational support for a flat core at the center of galactic
dark matter (DM) halos. We use detailed cosmologically motivated numerical
models to investigate the systematics and the accuracy of recovering parameters
of the galaxies. Some of our models match the observed structure of the two
galaxies remarkably well. Our analysis shows that the rotation curves of these
two galaxies are instead quite compatible with their DM halos having steep
cuspy density profiles. The rotation curves in our models are measured using
standard observational techniques. The models reproduce the rotation curves of
both galaxies, the disk surface brightness profiles as well as the profile of
isophotal ellipticity and position angle. The models are centrally dominated by
baryons; however, the dark matter component is globally dominant. The simulated
disk mass is marginally consistent with a stellar mass-to-light ratio in
agreement with the observed colors. We show that non-circular motions combined
with gas pressure support and projection effects results in a large
underestimation of the circular velocity in the central $\sim 1$ kpc region,
creating the illusion of a constant density core. Although the systematic
effects mentioned above are stronger in barred systems, they are also present
in axisymetric disks. Our results strongly suggest that there is no
contradiction between the observed rotation curves in dwarf galaxies and the
cuspy central dark matter density profiles predicted by Cold Dark Matter
models.
