The detections of both X-ray and radio emission from the cluster G1 in M31 have provided strong support for existing dynamical evidence for an intermediate mass black hole (IMBH) of mass 1.8 +/- 0.5 x 10^4 solar masses at the cluster center. However, given the relatively low significance and astrometric accuracy of the radio detection, and the non-simultaneity of the X-ray and radio measurements, this identification required further confirmation. Here we present deep, high angular resolution, strictly simultaneous X-ray and radio observations of G1. While the X-ray emission (L_X = 1.74^{+0.53}_{-0.44} x 10^{36} (d/750 kpc)^2 erg/s in the 0.5-10 keV band) remained fully consistent with previous observations, we detected no radio emission from the cluster center down to a 3-sigma upper limit of 4.7 microJy/beam. Our favored explanation for the previous radio detection is flaring activity from a black hole low mass X-ray binary (LMXB). We performed a new regression of the Fundamental Plane of black hole activity, valid for determining black hole mass from radio and X-ray observations of sub-Eddington black holes, finding log M_{BH} = (1.638 +/- 0.070)log L_R - (1.136 +/- 0.077)log L_X - (6.863 +/- 0.790), with an empirically-determined uncertainty of 0.44 dex. This constrains the mass of the X-ray source in G1, if a black hole, to be <9700 solar masses at 95% confidence, suggesting that it is a persistent LMXB. This annuls what was previously the most convincing evidence from radiation for an IMBH in the Local Group, though the evidence for an IMBH in G1 from velocity dispersion measurements remains unaffected by these results.