It's absolutely accurate, you're just missing the fact that H2 and O2 have to oxidize, aka "burn," to create that bond. Literally the easiest way to "create" water is to take a flask of pure hydrogen, a flask of pure oxygen that contains roughly 2.5 times the hydrogen vs oxygen to account for inefficiencies, "pour" those flasks into a container, and light it on fire. The ensuing explosion will convert almost all the hydrogen and most of the oxygen into water. Please stand well back, like behind a reinforced bunker wall if you attempt this.

Forming that bond frees up a single Oxygen atom, splitting the bond it has with its partner and causing a reaction that ends up releasing the excess energy of the Oxygen molecule, and bonding one of the Oxygen atoms to two Hydrogen atoms, the extra Oxygen atom then allows the oxidation process to happen. It also releases a large amount of energy, if you're a Hydrogen or Oxygen atom, or a tiny amount of mostly heat energy if you're a human. (Problem if you're a human is that you aren't capable of causing a single H2+O2+e→O1+H2O+e^x, so you're gonna get a large explosion for even small amounts of a mixture)

This is also true of all other "ash" products created by oxidization of pretty much any fuel from trees to iron. Once you "burn" the compound, it becomes chemically inert for further oxidation, because the atomic bonds of the molecules are about as stable as they can get.

This is why, chemically and physicsally speaking, burning or Oxidizing fuel creates plasma that we call fire. That plasma is the excess energy being expelled as the fuel combines with mostly Oxygen, to form ashes.

Water just happens to be the only type of ash we are familiar with that isn't dry, and instead gets things wet. There may be a few others, but I suspect that most of them are acids or bases that we don't regularly have any contact with.

Edit: source: former US Navy Nuclear Power Program Electronics Technician Instructor. I understand the physics involved, and can easily do the math that the chemistry uses. I don't know shit about biology, so there are probably some biological protein chains that negate literally everything I just said.

Edit 2: Sorry for the first 20 minutes, my comment was reversed with O2 and H2. I literally had to type out the math to remind myself how that reaction works.

As others said, hydrogen and oxygen gas in the same container will not create water until energy is put in. Fill a Ballon with a balloon with a 2:1 molar ratio of H2 and O2, then pop the Ballon with a flame, and you will get a cloud of water vapor. Without the fire, popping the balloons with a needle will only release the gases.