Storing hydrogen underground for cyclic injection/retrieval may help move the world towards a decarbonised economy. In search of suitable long-term reservoirs, the potential reactivity of the matrix with hydrogen plays a major role. This is especially poignant for carbonate minerals, due to their abundance, ubiquity, and much faster dissolution kinetics compared to silicates. Geochemical modelling studies invariably find hydrogen-induced reductive carbonate dissolution and methane production (HIRCDAMP) whereas experimental studies, for the most part, do not support this view. To answer the question of how far injected hydrogen may oxidise, protonate and cause reductive dissolution of carbonates, a thermodynamic approach based on standard redox and overall cell potentials, as well as Gibbs free energies, was chosen. Together with observations on kinetic constraints, a consistent picture emerges in which purely inorganically driven reduction of (bi)carbonate to methane by hydrogen oxidation is not likely to occur. Rather, the formation of intermediate carbon species (e.g., formate) could be a kinetically and thermodynamically more favourable pathway than that to methane. It follows that geochemical models that question the long-term viability of hydrogen injection into carbonate-bearing reservoirs need to be revised, toning down any alleged, yet by experimental studies not substantiated, hydrogen reactivity in the absence of any catalyst and/or microbial activity.