Adsorption of particles at oil-water interfaces is the basis of Pickering emulsions, which are common in nature and industry. For hydrophilic anionic particles, electrostatic repulsion and the absence of wetting inhibit spontaneous adsorption and limit the scope of materials that can be used in emulsion-based applications. Here, we explore how adding ions that selectively partition in the two fluid phases changes the interfacial electric potential and drives particle adsorption. We add oil-soluble tetrabutyl ammonium perchlorate (TBAP) to the nonpolar phase and Ludox silica nanoparticles or silica microparticles to the aqueous phase. We find a well-defined threshold TBAP concentration, above which emulsions are stable for months. This threshold increases with the particle concentration and with the oil's dielectric constant. Adding NaClO4 salt to water increases the threshold and causes spontaneous particle desorption and droplet coalescence even without agitation. The results are explained by a model based on the Poisson-Boltzmann theory, which predicts that the perchlorate anions (ClO4-) migrate into the water phase and leave behind a net positive charge in the oil. Our results show how a large class of inorganic hydrophilic, anionic nanoparticles can be used to stabilize emulsions in a reversible and stimulus-responsive way, without surface modifications.