We use measurements of the projected galaxy correlation function w_p and galaxy void statistics to test whether the galaxy content of halos of fixed mass is systematically different in low density environments. We present new measurements of the void probability function (VPF) and underdensity probability function (UPF) from Data Release Four of the Sloan Digital Sky Survey, as well as new measurements of the VPF from the full data release of the Two-Degree Field Galaxy Redshift Survey. We compare these measurements to predictions calculated from models of the Halo Occupation Distribution (HOD) that are constrained to match both w_p and the space density of galaxies. The standard implementation of the HOD assumes that galaxy occupation depends on halo mass only, and is independent of local environment. For luminosity-defined samples, we find that the standard HOD prediction is a good match to the observations, and the data exclude models in which galaxy formation efficiency is reduced in low-density environments. More remarkably, we find that the void statistics of red and blue galaxies (at L ~ 0.4L_*) are perfectly predicted by standard HOD models matched to the correlation function of these samples, ruling out "assembly bias" models in which galaxy color is correlated with large-scale environment at fixed halo mass. We conclude that the luminosity and color of field galaxies are determined predominantly by the mass of the halo in which they reside and have little direct dependence on the environment in which the host halo formed. In broader terms, our results show that the sizes and emptiness of voids found in the distribution of L > 0.2L_* galaxies are in excellent agreement with the predictions of a standard cosmological model with a simple connection between galaxies and dark matter halos. (abridged) Comment: 20 emulateapj pages, 9 figures. submitted to ApJ