Interatomic (or intermolecular) Coulombic decay is a general, very efficient mode of decay of inner valence vacancies in clusters. The physically appealing interpretation of such decays as a transfer of a virtual photon between two cluster units rests on the neglect of the orbital overlap between them. We show that even in loosely bound van der Waals clusters the orbital overlap is a crucial factor. At the equilibrium geometry of a cluster, the overlap effect can bring about an enhancement of the decay rate by 2-3 orders of magnitude, making the process dramatically more efficient than implied by the simple estimations.