He measured the water level to be sure there was no recombination. You claim that evaporation at any power level might magically remove just enough water to hide recombination. That's impossible. The temperatures during calibration and during the run with both the active and control cells varied over a wide range, so any evaporation would have varied. It could not magically equal recombination, because recombination is not governed by temperature. Again, if you dispute this, I suggest you do a simple experiment and see for yourself.
As you know I have commercial/technical interests in the hydrogen business. The problem of what is called 'gas crossover' in large electrolytic systems is known and has been studied extensively because it costs companies money. So I have been digging around in the published research. From this it appears that the the predominant mechanism is gas crossover of oxygen and the resulting catalytic formation of hydrogen peroxide at the anode side of the cell. Which is endothermic.
They don't worry so much about recombination at the cathode, which is considered to be insignificant, and as one paper mentions it actually produces current which in turn splits more water, something which reduces the effect of recombination upon system efficiency.