We present a core level X-ray photoelectron spectroscopy study of NixMg12xO crystals with 0.03<x<1. We show that nonlocal effects involving inter-Ni-site fluctuations strongly influence the Ni 2p core-level spectra for higher Ni concentrations including NiO itself. It is only in the very dilute Ni limit that the core-level spectra can be described in terms of an Anderson impurity model which also must include a realistic band structure for the O 2p. Moreover, it is only in this limit that a single-site model can explain the core-level and valence-band spectra as well as the optical data by using one consistent set of parameter values. These results consolidate the concepts of nonlocal screening and provide a better understanding of the electronic structure of NiO.