The issue is that it is trivial to perform electrolysis at room temperature, in pH neutral water. Drop a 9v battery in a clear glass of salted water and watch. You will (slowly) get hydrogen gas. Oxygen you may not get depending on what battery leads are made of... you may just get some corrosion, and in any case most of the energy is lost as heat (salt water conducts).
Which gets me back to those catalysts! I'll see if they published anything about that in a peer-reviewed journa