This is the first I've ever heard of the theory that grains volume of black powder actually refers to the volume of that many grains of water. I'm not sure I'm going to accept that idea at this time.
Let's give an example. The .45 Colt, according to my Lee's reloading manual, has a "useful case capacity" (whatever that means) of 1.93cc. Due to the wonders of the metric system that means it would also hold almost exactly 1.93 grams of water. (They set the system up to have that correlation be exact, but this was in the 18th Century. Their measurements were just a bit less precise than ours today.)
1.93 grams of water at 15.432 grains/gram (see
www.onlineconversion.com) comes out to 29.78 grains of water. The historical charge for the .45 Colt was supposed to be 40 grains black powder. Modern cartridges have more brass and therefore less volume, but according to some websites I've checked they are still getting 36 or 37 grains of BP into their .45 Colt loads.
So the correlation between grains weight of water and blackpowder grains measured by volume is vaguely close, but only vaguely.
That line about "Can you imagine weighing out powder in the heat of battle, or to get a second shot at a deer?" is correct enough. Thing is, though, that there would have been no need to calibrate a dipper or scoop or what have you to some volume based on some set weight of water.
The hunters weren't that precise. They would have started with some rule of thumb-- one of the old ones is, put a round ball in the palm of your hand and pour powder over it until the ball is just covered by the heap, and that's your load. They'd use some starting point like that, and hollow out a little cup or dipper of that volume, or a little more, or a little less, based on what they thought worked best with their particular gun. Or if the weapon came from a factory packed with all the accessories, some sort of dipper or powder flask spout of the "proper" volume might come with the kit. Calibrating those measures to a certain weight of black gunpowder itself was as easy as anything else, assuming the measures weren't homemade. If they were homemade, they might not have been calibrated to anything at all.
As for the military, at least as far back as the American Revolution governments provided their soldiers with pre-measured gunpowder charges. The powder came in a paper tube cartridge along with the appropriate projectile or projectiles. You bit the end off the tube, poured the powder down the barrel, rammed the ball down on top, and there you were. Again, there's no need to provide any information correlating the volume of the powder with the weight of that volume of water. It's really an unnecessary step.