We present optical and near-IR spectroscopic observations of the luminous blue variable SN 2009ip during its remarkable photometric evolution of 2012. The spectra sample three key points in the SN 2009ip lightcurve, corresponding to its initial brightening in August (2012-A) and its dramatic rebrightening in early October (2012-B). Based on line fluxes and velocities measured in our spectra, we find a surprisingly low I(H-alpha)/I(H-beta) ~ 1.3-1.4 in the 2012-B spectra. Such a ratio implies either a rare Case B recombination scenario where H-alpha, but not H-beta, is optically thick, or an extremely high density for the circumstellar material of n_e > 10^13 cm^(-3) The H-alpha line intensity yields a minimum radiating surface area of >~20,000 AU^2 in H-alpha at the peak of SN 2009ips photometric evolution. Combined with the nature of this objects spectral evolution in 2012, a high circumstellar density and large radiating surface area imply the presence of a thin disk geometry around the central star (and, consequently, a possible binary companion), suggesting that the observed 2012-B rebrightening of SN 2009ip can be attributed to the illumination of the disks inner rim by fast-moving ejecta produced by the underlying events of 2012-A.