Abstract Dedicated searches generally find a decreasing fraction of obscured active galactic nuclei (AGN) with increasing AGN luminosity. This has often been interpreted as evidence for a decrease of the covering factor of the AGN torus with increasing luminosity, the so-called receding torus models. Using a complete flux-limited X-ray selected sample of 199 AGN, from the Bright Ultra-hard XMM-Newton Survey, we determine the intrinsic fraction of optical type-2 AGN at as a function of rest-frame 2–10 keV X-ray luminosity from to . We use the distributions of covering factors of AGN tori derived from CLUMPY torus models. Since these distributions combined over the total AGN population need to match the intrinsic type-2 AGN fraction, we reveal a population of X-ray undetected objects with high-covering factor tori, which are increasingly numerous at higher AGN luminosities. When these “missing” objects are included, we find that Compton-thick AGN account at most for % of the total population. The intrinsic type-2 AGN fraction is 58 ± 4% and has a weak, non-significant (less than 2σ) luminosity dependence. This contradicts the results generally reported by AGN surveys and the expectations from receding torus models. Our findings imply that the majority of luminous rapidly accreting supermassive black holes at reside in highly obscured nuclear environments, but most of them are so deeply embedded that they have so far escaped detection in X-rays in <10 keV wide area surveys.