At the moment this is an absolute record for energy costs with “cold fusion” Low Energy Nuclear Reaction (LENR). It outpaces all research centers, laboratories and universities involved in the hydrogen problem of (LENR) for 20-30 years
In retrospect, it looks like they were talking about someone else; the text isn't all that clear.
Back to the original issue: The Second Law of Thermodynamics says that you will always get less energy from burning hydrogen than it took to separate it from water; in effect, hydrogen becomes a battery. If these people have a way to use solar energy to economically power hydrogen separation, they'd probably be better of just selling the solar power. Sorry, but this whole thing reeks of scam.
First, they don't have a way to use solar power to do hydrolysis, and don't claim to. They claim to be "transmuting oxygen into hydrogen."
Second, if we stipulate to a hypothetical [just for the sake of discussion] the process could actually be useful because, while you do lose energy in the form of heat in the process, that doesn't matter; the energy you've used to create the hydrogen is solar, so it's "free." The hydrogen freed by the process would be useful as a storage medium that Greenies would like, because it has "no carbon," unlike gasoline, which is essentially a hydrogen storage medium [also produced by solar energy] which releases carbon by-products on combustion.
Third. Despite what Greenies like, any process involving hydrogen as an energy storage medium is stupid (it is not a primary energy source on Earth, since all the free hydrogen on this planet bonded with other elements long ago or escaped into space.)
Why is it stupid? Because it has only about 1/4 of the energy density of gasoline when compressed and liquefied. A hydrogen "gas tank" would take you 1/4 of the distance without refueling. Worse, about half of the energy required to deliver hydrogen in usable form is burned up in the process of compressing the gas.
So, the Second Law is not the issue, because the hydrogen is produced via solar energy, and the energy available is "all net." Solar energy has to be stored somehow, and hydrogen "sounds good" as an energy storage material. But it isn't.
Again, the existence of the sun and our atmosphere) within our local earthly system gets us around the second law of thermodynamics by providing near limitless energy to throw back into the system and, thereby, “fight off” the increasing entropy that would otherwise occur. It does not allow us to violate the law, but it gives us the energy to avoid its reality.