This is true but misses the point. As I said in my previous post, it takes more energy to extract hydrogen from water than you get back from the hydrogen (the point which you then restated in the above quoted language).
But the opposite is true for extracting oil from the ground or digging uranium--it takes less energy to extract than you get burning it. That's why nuclear can replace oil as a primary energy source and why hydrogen is only an storage medium for energy obtained from primary energy sources--a battery.
Do you really believe that hydrogen is an alternative to oil in the sense that it could act as a primary energy source? If not, I don't understand your initial point--that is, hydrogen should be set up as a competitor to oil. Even if we had an intact hydrogen infrastructure (so I've just saved you billions of dollars) hydrogen can't compete with nuclear and oil because we would still have to get the energy somewhere to store in the form of elemental hydrogen. And that somewhere would almost certainly be nuclear and fossil fuel.
If your point was that oil is a battery too, that is technically correct. Oil contains stored energy from the sun and geologic processes. But that's on a time scale of hundreds of millions of years--not really relevant to this discussion.