I understand, you mean no direct water is added. Looked up the saponifying process and found that it basically makes soap,
water and glycerine. That probably is part of the water content.
"Soap is made by saponifying a fat or oil with a strong alkali. A fat or oil is a triglyceride, which means that three fatty acids of various carbon lengths are attached to a glycerine backbone. The strong alkali is either sodium (for bars) or potassium (for liquids) hydroxide. The saponification process is a simple one-step reaction with no waste generated: the glycerine is split off from the fatty acids, and the fatty acids combine with the sodium or potassium to form soap, while the hydroxide forms water. The result is soap, glycerin and water (no alkali remains). "
More water would be in the Aloe Vera as it is normally 96% water. You don't really have to add pure water to have a water content.
Almost any liquid winds up having water as a basic ingredient. Sort of like looking at dog food ingredients. Most canned food lists water as the first ingredient. Some of the premium dog foods don't list water but they do list chicken broth -- that is mostly water.
I did wonder about the high Ph for the shampoo. It is unusal for the ph to be that high for a dog shampoo. Why did you decide on that and how does it not have detrimental effects? Since you researched I know you have a reason behind this. Just thought I would ask. Too high of a ph is said to have harmful side effects, strip away some of the necessary oils on a dog's skin, and leaving a dog with dry, irritated skin, causing extra itchiness and scratching. Too high of a ph can weaken the hair by breaking the disulfide bonds in hair keratin.
Referenced from:
About Dog Shampoo | DailyPuppy.com
Another site discussed making your own dog shampoo but cautioned that when using Ivory dish detergent (with a ph of 9.5) as one of the ingredients, you must add: 2 teaspoons of white vinegar along with the required teaspoon of glycerin. This will bring the pH down to 6.8 which is well within the realm of a dog’s skin.
Dog shampoo-Make your own, easy & inexpensive[B]
I brought up that last example as it is close to the Ph of 9 you shampoo has and they are recommending adding vinegar to bring the ph down to 6.8. Not that I want to make my own shampoo with Ivory.
Thanks!