  We use Bogoliubov de-Gennes theory to show that the commonly used
Thomas-Fermi approximation (TFA) can fail in describing polarized unitary gases
in anisotropic harmonic traps. We find a magnetized superfluid region inside
the trap, with order parameter oscillations, even though there is no such
stable bulk phase. This leads to magnetization profiles that deviate from
contours of constant potential energy. We determine how this violation scales
with trap anisotropy and number of particles, and show that we are able to
account for important differences between the MIT and Rice experiments.
