Zero-point calibration priors vs. posteriors for each Rubin filter. The unified fitting framework allows for self-calibration, reducing posterior uncertainties by up to 40% relative to the assumed priors. However, we find no floor beyond which the posterior uncertainty is always lower than the prior uncertainty for any realistic prior. This indicates a potential prior-dependence of cosmology results in hierarchical Bayesian frameworks even after self-calibration, and warrants further investigation.