In a simple model for the long-time dynamical behavior of Brownian suspensions, particles diffuse independently while simultaneously undergoing direct interactions with each other. Despite its simplicity, this model forms the basis of both the Brownian dynamics computer simulation technique and apparently successful theories. Here we use the approach to study numerically the viscoelastic response of a suspension of hard spheres. At low volume fractions (10%) we find that the frequency dependence of the viscosity is in agreement with theoretical calculations based on solving the two-particle Smoluchowski equation. At a higher volume fraction (45%) we find that the model is not well described by various extensions of low density theory that have been proposed. Including hydrodynamics in a minimal way (by allowing the particles to diffuse with the short-time diffusion coefficient! and comparing with experiment, the model successfully reproduces the viscoelastic response over an intermediate range of frequencies. However, at low frequencies a significant disagreement emerges. A "slowing down'' of the dynamics of the particles at longer times, more apparent in the simulations than in the experimental results, appears to be the cause of this discrepancy. Ultimately, this leads to a significant overestimate of the zero frequency (Newtonian) viscosity. The reason theories based on the approach yield such excellent agreement with experiment, we can only conclude, is because they fail to describe the model adequately.