The paper examines the robustness of cosmological neutrino mass bounds, particularly the stringent limit of \(\sum m_{\nu} < 0.072 \, \text{eV}\) at 95% CL derived from Planck 2018+ACT lensing+DESI data. This limit is very close to the minimum possible sum of neutrino masses, suggesting vanishing or even negative cosmological neutrino masses. The authors investigate three aspects: (i) the role of potential anomalies in Planck CMB and DESI BAO data; (ii) the comparison between frequentist and Bayesian techniques; and (iii) the impact of deviations from the standard \(\Lambda\)CDM model. They find that the preference for negative neutrino masses is largely due to the Planck 2018 data, which includes the well-known 'lensing anomaly'. This preference disappears when using the new Planck 2020 HiLiPoP data, leading to weaker constraints. Additionally, the tension between DESI data and Planck at \(z = 0.7\) is significant, and removing these outliers relaxes the bound to \(\sum m_{\nu} < 0.11 \, \text{eV}\) at 95% CL. The preference for dynamical dark energy further weakens the bound. The study highlights the importance of carefully evaluating the origin and behavior of cosmological constraints on neutrino masses, especially as future data may confirm or refute these trends.The paper examines the robustness of cosmological neutrino mass bounds, particularly the stringent limit of \(\sum m_{\nu} < 0.072 \, \text{eV}\) at 95% CL derived from Planck 2018+ACT lensing+DESI data. This limit is very close to the minimum possible sum of neutrino masses, suggesting vanishing or even negative cosmological neutrino masses. The authors investigate three aspects: (i) the role of potential anomalies in Planck CMB and DESI BAO data; (ii) the comparison between frequentist and Bayesian techniques; and (iii) the impact of deviations from the standard \(\Lambda\)CDM model. They find that the preference for negative neutrino masses is largely due to the Planck 2018 data, which includes the well-known 'lensing anomaly'. This preference disappears when using the new Planck 2020 HiLiPoP data, leading to weaker constraints. Additionally, the tension between DESI data and Planck at \(z = 0.7\) is significant, and removing these outliers relaxes the bound to \(\sum m_{\nu} < 0.11 \, \text{eV}\) at 95% CL. The preference for dynamical dark energy further weakens the bound. The study highlights the importance of carefully evaluating the origin and behavior of cosmological constraints on neutrino masses, especially as future data may confirm or refute these trends.