Electrolysis of water

In a previous post, I stated that steam methane reforming requires only half the energy of the electrolysis of water.  The so-called hydrogen economy will be a topic that I will come back to from time to time, and while doing more calculations, I may have encountered an error in the numbers.  It is important to always present accurate information—my goal is, of course, to promote education and critical thinking.

Steam methane reforming is a process in which natural gas and water are placed under high temperature—up to 1000 degrees Celsius—and pressure.  This ensures that the reactants are fully converted into hydrogen and carbon dioxide.
$$ \text{CH}_4 + 2 \text H_2 \text O + 165 \text{ kJ} \rightarrow \text{CO}_2 + 4 \text H_2 $$This source claims that the process requires approximately 135 megajoules (MJ) of energy.  However, my best efforts cannot reconcile this with naïve thermo-chemistry.  Using the enthalpy of formation, I can only account for 21 MJ per kilogram of hydrogen.  Even including all the heat required to create the high temperatures needed does not reconcile the difference.

Electrolysis, as the name implies, involves the use of electricity to disassociate the oxygen and hydrogen in water.  Though this process can be demonstrated without high temperatures in table-top experiments, industrial applications often require them.$$2 \text{H}_2\text{O} + 484 \text{ kJ} \rightarrow \text{O}_2 + 2 \text{H}_2$$Because of the stability of the bonds in water, the energy requirement is considerably larger than steam reformation.  Naïve thermo-chemistry yields about 120 MJ per kilogram of hydrogen.  I am unable to find sources that give the energy requirements for the industrial state of the art.  From a purely theoretical stand point, though, steam reformation has only one fifth the energy requirement of electrolysis.  Furthermore, if electrolysis could more easily manufacture hydrogen, we would already use this method more widely; though, it remains unclear exactly how different the energy requirements are.