It is shown that exactly the same results of the modified integral encounter theory (MET) of diffusion-influenced reactions can be derived from the nonequilibrium reduced distribution function (RDF) theory. The method of solution of the RDF theory is much simpler than that of the MET, and shows clearly that the sophisticated approximation scheme employed in the latter is effectively equivalent to a simple truncation approximation adopted in the former. We evaluate the relative accuracy of the various theories by comparing the theoretical results with the results of an accurate Brownian dynamics simulation and the exact theory that are available for simple reaction models.