Our work provides two major insights: First, we demonstrate that interfacial water at Pt(111) does not behave as expected from classical considerations as a perfect conductor separated by a sharp transition boundary from a perfectly insulating, dielectric material. Instead, we find that the electronic excess charge density exhibits a double-peaked structure, where a significant amount of 30 -40% of excess charge localizes within the first, interfacial water (bi)layer and only 60 -70% within the (leaking) metal region. These results are in line with previous reports of a non-vanishing, local density of states at the Fermi level within interfacial water and likely explain partially charged interfacial ions, in particular protons at Pt(111) . Second, we analyze in detail how the electrostatics by these extended electron distributions lead to significantly larger interfacial capacitances than rationalizable classically and accordingly modeled with common force fields. As a result, electronic structure methods lead to realistically high interfacial capacitances of Pt(111) that are significantly higher (∼ 10×!) than those from FF-based methods. While a range of recent works have equally identified electron leakage into the non-metallic region of space as the predominant factor behind the dramatic failure of FF simulations, our present comparison of electron leakage at Pt interfaced with vacuum and water highlights that interfacial water is instrumental to understand the significant charge leakage at the Pt(111)-water interface.