In a recent paper in this journal, proton transport in oxides was considered in terms of density functional theory and the non-adiabatic Flynn–Stoneham approach of small polaron type proposed much earlier for metals. Also, regimes of hydrogen diffusion relevant to oxides were reviewed, but the straightforwardly observable channel of low-temperature over-barrier jumps has passed unnoticed. We offer this latter possibility, together with some additional arguments, to make our objection more compelling. There are two major contentious findings in the article. First, in discussing the phonon-assisted quantum regime and the adiabatic coincidence configuration in barium stannate, the article claimed that the models based on a fully non-adiabatic picture for metals cannot be generalized to proton-conducting oxides. It is difficult to agree with such a viewpoint because such generalizations are being published. By means of a counterexample, this comment illustrates the real efficacy of using Flynn–Stoneham-like models in studying these oxides. Second, we have strong grounds for supposing that the main claim of the paper being commented on about the adiabatic nature of the proton transfer is in conflict with general interpretation of small polaron hopping. The exact knowledge of energy barriers for proton transfer is needed to confirm the validity of assuming an adiabatic regime. Since the most likely influence of the functional on the adiabaticity criterion formulation is certainly evident, comparison of the results of Geneste et al. to results obtained with higher functionals may check the validity of the present GGA-PBE scheme.