© 2020 The Royal Society of Chemistry. Anions generally associate more favorably with the air-water interface than cations. In addition to solute size and polarizability, the intrinsic structure of the unperturbed interface has been discussed as an important contributor to this bias. Here we assess quantitatively the role that intrinsic charge asymmetry of water's surface plays in ion adsorption, using computer simulations to compare model solutes of various size and charge. In doing so, we also evaluate the degree to which linear response theory for solvent polarization is a reasonable approach for comparing the thermodynamics of bulk and interfacial ion solvation. Consistent with previous works on bulk ion solvation, we find that the average electrostatic potential at the center of a neutral, sub-nanometer solute at the air-water interface depends sensitively on its radius, and that this potential changes quite nonlinearly as the solute's charge is introduced. The nonlinear response closely resembles that of the bulk. As a result, the net nonlinearity of ion adsorption is weaker than in bulk, but still substantial, comparable to the apparent magnitude of macroscopically nonlocal contributions from the undisturbed interface. For the simple-point-charge model of water we study, these results argue distinctly against rationalizing ion adsorption in terms of surface potentials inherent to molecular structure of the liquid's boundary.