From a profile likelihood analysis, we derive constraints in agreement at the ∼10% level with Bayesian posteriors. We find that the weak preference for negative neutrino masses is mostly present for Planck 18 data, affected by the well-known "lensing anomaly". It disappears when the new Planck 2020 HiLLiPoP is used, leading to significantly weaker constraints. Additionally, the pull towards negative masses in DESI data stems from the z=0.7 bin, which is in ∼3σ tension with Planck expectations. Without these outliers, and in combination with HiLLiPoP, the bound relaxes to ∑mν<0.11eV at 95% CL. The recent preference for dynamical dark energy alleviates this tension and further weakens the bound. As we are at the dawn of a neutrino mass discovery from cosmology, it will be very exciting to see if this trend is confirmed by future data.