I'll dispute the first sentence as well. The "nuclear" part of "from nuclear and coal-fired power plants, which would make it really dirty energy" is nonsense. Nuclear power is one of the cleanest forms of energy we have, even just measuring on radioactive pollution alone (the average coal plant puts out more radioactives in a year than a nuke plant will throughout it's lifespan). The problem with nuclear power is political, not technical.
The fact is that, unless the law of conservation of energy is repealed, hydrogen will always require more energy to produce than it will provide.
While hydrogen is generally considered a fuel transport mechanism rather than a fuel source, this statement isn't completely true either. It would be true if you got the hydrogen from a source like water, but it is possible to obtain the hydrogen from natural gas instead (providing more energy than required to produce it). Of course, natural gas supplies aren't infinite, but it would be trivial to access methane hydrate supplies off the coast (providing enough energy for a few thousand years or longer) once the supply of easily exploitable natural gas is expended.
The problem with nuclear power is public ignorance and fear.