Many modern simulations of accretion disks use moment-based methods for radiation transport to determine the thermal evolution of the disk and the properties of the ejected matter. The popular M1 scheme evolves the rank-0 and rank-1 moments requires an analytic approximation for the rank-2 and higher tensors. We present the open-source Monte Carlo steady-state general-relativistic neutrino transport code SedonuGR, which we use to asses fundamental analytic closure assumptions, quantify proposed closure errors, and test an extension of the MEFD closure to the rank-3 moment. We demonstrate that the fundamental assumptions employed in all analytic closures are strongly violated. This violation is most evident at the interface between the equatorial disk and the evacuated polar regions. Finally, we calculate the neutrino momentum and energy deposition rate from neutrino pair annihilation, and demonstrate that a moment-based annihilation power calculation is accurate to at most ~20% if the rank-2 and higher moments are neglected. Out of a selection of 8 closures in the literature, we demonstrate that different closures reproduce different aspects of the radiation field (pressure tensor, rank-3 tensor, pair annihilation rate), though the MEFD, Levermore, and Janka 2 closures are all reasonable. The extra information from the neutrino degeneracy used in the MEFD closure is unable to account for the diversity in the rank-2 and rank-3 moments.