  Even though SN 2012cg is one of the best-studied Type Ia Supernovae to date,
the nature of its progenitor system has been debated in numerous studies.
Specifically, it is difficult to reconcile recent claims of the detection of a
$\sim 6 \rm{M}_\odot$ main-sequence companion with recent deep, late-time
H$\alpha{}$ flux limits. In this study we add three new constraints: 1) We
analyze new high-signal-to-noise, nebular-phase, LBT/MODS spectrum of SN 2012cg
and place an upper limit on the amount of low-velocity, solar-abundance
material removed from a possible companion of $ < 7.8 \times 10^{-3}
\rm{M}_\odot$. 2) We use Swift X-ray observations to constrain the preexplosion
mass-loss rate to be $\dot M<10^{-6}\,$ $\rm{M}_\odot$ yr$^{-1}$ for
$v_\textrm{w}=100\,\rm{km\,s^{-1}}$. 3) We carefully reanalyze a prediscovery
MASTER image and, with published light curves of SN 2012cg, we estimate the
time of first light and conservatively constrain the radius of a Roche-lobe
overflowing companion to be $< 0.24 \rm{R}_\odot$. These observations disagree
with a large nearby companion, and, when considered with other studies of SN
2012cg's progenitor system, essentially rule out a non-degenerate companion.
