Observations by the James Webb Space Telescope of the Universe at $z\gtrsim 4$ have shown that massive black holes (MBHs) appear 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. Understanding how such objects formed and grew to this masses has then become a big challenge for theoretical models, with different ideas ranging from heavy seed to super-Eddington accretion phases. Here, 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, up to an order of magnitude, and a potential preference for lower masses and higher accretion rates, which i) move them closer to the local correlations, and ii) might indicate that we are witnessing for the first time a widespread phase of very rapid accretion.