The phrase "dielectric friction" tends to bring to mind the drag force exerted by a polar liquid on some translating ion or rotating dipolar molecule, but the underlying idea is far more general. Any relaxation process taking place in a polar environment, including those involving solvation and vibrational relaxation, has the potential to be strongly affected by the special dynamics associated with Coulombic forces. Indeed, there is considerable evidence that vibrational energy relaxation is noticeably accelerated in hydrogen-bonding solvents. What is less clear is precisely how electrostatic forces achieve the accelerations they do and to what extent this phenomenon relies on specifically protic solvents. We explore this issue in this paper by using classical molecular dynamics to study the vibrational population relaxation of diatomic solutes with varying levels of polarity dissolved in both dipolar and nondipolar aprotic solvents. We find that the conventional analysis based on partitioning the force autocorrelation function can be usefully extended by adapting an instantaneous perspective; distinguishing between the purely equilibrium effects of the instantaneous liquid structure surrounding a solute and the solely nonequilibrium effects of the relaxation dynamics launched from those initial conditions. Once one removes the powerful influence of electrostatic forces on the liquid structure, either by simple normalization or by looking at the "force-velocity" autocorrelation function, the subsequent dynamics (and therefore the mechanism) of the relaxation is revealed to be dominated by short-ranged repulsive forces, even under the most polar circumstances. The main rate-enhancing effect of Coulombic forces seems to be an equilibrium electrostriction: The solvent is simply ordered around the solute in such a way as to amplify the repulsive forces. At least in our examples, the slowly varying character of Colombic forces actually makes them quite ineffective at any kind of direct promotion of vibrational energy relaxation.