Observations by the James Webb Space Telescope of the Universe at z≳4 have shown that massive black holes (MBHs) appear to be extremely overmassive compared to the local correlation for active galactic nuclei. In some cases, these objects might even reach half the stellar mass inferred for the galaxy. It has become a great challenging for theoretical models to understand how these objects formed and grew to these masses. Different ideas range from heavy seed to super-Eddington accretion phases. We take a different approach and try to infer how accurate these MBH mass estimates are and whether we really need to revise our physical models. By considering how the emerging spectrum (both the continuum and the broad lines) of an accreting MBH changes close to and above the Eddington limit, we infer a much larger uncertainty in the MBH mass estimates relative to that of local counterparts. The uncertainty is up to an order of magnitude. We also infer a potential preference for lower masses and higher accretion rates, which i) moves accreting MBHs closer to the local correlations, and ii) might indicate that we witness a widespread phase of very rapid accretion for the first time.