We study the electrostatic interaction between two ionic surfactant layers by performing molecular dynamic simulations of salt-free thin water films coated by surfactants (Newton black films). We find a strong exponentially decaying short-range repulsion not explained by classical Poisson-Boltzmann theory. This electrostatic force is shown to be mainly due to the anomalous dielectric response of water near charged surfactant layers. This result clarifies the much debated physical mechanism underlying the controversial "hydration forces" observed in experiments. In the case of ionic thin films, the "hydration forces" can be identified with the electrostatic forces induced by the layers of highly polarized water originated at the interfaces.