Ionic liquids represent a novel and poorly understood class of solvents, and one challenge in understanding these systems is how one should view the electrostatic character of solute-solvent interactions. The highly structured nature of a fused salt makes a dielectric continuum approximation difficult to implement, and there is no obvious connection between the structure of an individual ion and the polarization character of the medium. We address this problem by making the ansatz that rather than polarizing the medium, the solute may be viewed as intercalating in the charge distribution of the neat liquid such that the solvent screens the electric field of the solute. This approach allows derivation of an analytical expression for the distribution of solvent charge about the solute, and this distribution is found to be a close match to simulation data. The theory also predicts that the electrostatic character of solute-solvent interactions should be determined primarily by the number density of solvent ions, a prediction proven correct by analysis of existing experimental data. The approach represents a new model for the interpretation of solvation phenomena in ionic liquids.