We show that the broad X-ray photoelectron lines of silicon oxide on silicon arise from a continuous statistical distribution of core-level binding energies. Statistical simulations spanning compositions from Si to SiO_2 reproduce the full extent of this broadening, reaching 5 eV for SiO_1.0 , in quantitative agreement with 0.23 nm layer-resolved spectra reconstructed from Ar^+ sputtering data. This continuous distribution blurs distinct spectral fingerprints of local structural motifs, thereby challenging conventional chemical state assignment in oxide X-ray photoelectron spectra.