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 ∼6 MS companion with recent deep, late-time flux limits. In this study we add three new constraints. (1) We analyze a new high-signal-to-noise, nebular-phase, Large Binocular Telescope/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 . (2) We use Swift X-ray observations to constrain the pre-explosion mass-loss rate to be for . (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 . 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.