Electrophoresis is widely used to determine the electrostatic potential of colloidal particles. Oil droplets in pure water show negative or positive electrophoretic mobilities depending on the pH. This is commonly attributed to the adsorption of hydroxyl or hydronium ions, resulting in a negative or positive surface charge, respectively. This explanation, however, is not in agreement with the difference in isoelectric point and point of zero charge observed in experiment. Here we present molecular dynamics simulations of oil droplets in water in the presence of an external electric field but in the absence of any ions. The simulations reproduce the negative sign and the order of magnitude of the oil droplet mobilities at the point of zero charge in experiment. The electrostatic potential in the oil with respect to the water phase, induced by anisotropic dipole orientation in the interface, is positive. Our results suggest that electrophoretic mobility does not always reflect the net charge or electrostatic potential of a suspended liquid droplet and, thus, the interpretation of electrophoresis in terms of purely continuum effects may need to be reevaluated.