  The question of the existence of active tidal disruption around various dSph
galaxies remains controversial. That debate often centers on the nature (bound
vs. unbound) of extended populations of stars. However, the more fundamental
issue of the very existence of the extended populations is still contentious.
We present an evaluation of the debate centering on one particular dSph,
Carina, for which claims both for and against the existence of stars beyond the
King radius have been made. Our review includes an examination of all previous
studies bearing on the Carina radial profile and shows that the survey method
which achieves the highest detected dSph signal-to-background in the outer
parts of the galaxy is the Washington M, T2 + DDO51 (MTD) filter approach from
Paper II in this series. We then address statistical methods used to evaluate
the reliability of MTD surveys in the presence of photometric errors and for
which a new, a posteriori statistical analysis methodology is provided.
Finally, these statistical methods are tested by new spectroscopy of stars in
the MTD-selected Carina candidate sample. Of 74 candidate giants with follow-up
spectroscopy, the MTD technique identified 61 new Carina members, including 8
stars outside the King radius. From a sample of 29 stars not initially
identified as candidate Carina giants but that lie just outside of our
selection criteria, 12 have radial velocities consistent with membership,
including 5 extratidal stars. Carina is shown to have an extended population of
giant stars extending to a major axis radius of 40' (1.44x the nominal King
radius).
