We performed molecular simulations to study ion pairing in aqueous solutions. Our results indicate that ion specific interactions of Li+, Na+, and K+ with the dimethyl phosphate anion are solvent-mediated. The same mechanism applies to carboxylate ions, as has been illustrated in earlier simulations of aqueous alkali acetate solutions. Contact ion pairs play only a minor role or no role at all in determining the solution structure and ion specific thermodynamics of these systems. On the basis of the Kirkwood Buff theory of solution we furthermore show that the well-known reversal of the Hofmeister series of salt activity coefficients, comparing chloride or bromide with dimethyl phosphate or acetate, is caused by changing from a contact pairing mechanism in the former system to a solvent-mediated interaction mechanism in the latter system.