Resistive random access memory is a promising, energy-efficient, low-power "storage class memory" technology that has the potential to replace both flash storage and on-chip dynamic memory. While the most widely employed systems exhibit filamentary resistive switching, interface-type switching systems based on a tunable tunnel barrier are of increasing interest. They suffer less from the variability induced by the stochastic filament formation process and the choice of the tunnel barrier thickness offers the possibility to adapt the memory device current to the given circuit requirements. Heterostructures consisting of a yttria-stabilized zirconia (YSZ) tunnel barrier and a praseodymium calcium manganite (PCMO) layer are employed. Instead of spatially localized filaments, the resistive switching process occurs underneath the whole electrode. By employing a combination of electrical measurements, in operando hard X-ray photoelectron spectroscopy and electron energy loss spectroscopy, it is revealed that an exchange of oxygen ions between PCMO and YSZ causes an electrostatic modulation of the effective height of the YSZ tunnel barrier and is thereby the underlying mechanism for resistive switching in these devices.