We perform a global χ² analysis of nuclear parton distribution functions using data from charged current neutrino-nucleus (νA) deep-inelastic scattering (DIS), charged-lepton-nucleus (ℓ(±)A) DIS, and the Drell-Yan (DY) process. We show that the nuclear corrections in νA DIS are not compatible with the predictions derived from ℓ(±)A DIS and DY data. We quantify this result using a hypothesis-testing criterion based on the χ² distribution which we apply to the total χ² as well as to the χ² of the individual data sets. We find that it is not possible to accommodate the data from νA and ℓ(±)A DIS by an acceptable combined fit. Our result has strong implications for the extraction of both nuclear and proton parton distribution functions using combined neutrino and charged-lepton data sets.