I think the article is ill informed & potentially misleading.
Let's recap some hair science.
pH scale is 1 to 14
7 is neutral
Less than 7 = acidic
Greater than 7 = alkaline.
Hair is between 4.5 - 5.5 (acid)
Tap water is around a 7 and this makes it more than 100 times more alkaline than hair. Therefore, washing your hair in just water will open up the cuticle and can make the hair swell by up to 20% of its volume.
(Hence the author of the article claiming her hair has more volume using her revolutionary cleaning regime!)
Hair conditioners are acidic.
Their main purpose is to close the cuticle which is essential after completing any chemical process. However, unless it's a 'leave in' conditioner, you are supposed to rinse the hair really thoroughly afterwards. Lots of clients don't do this very well at home particularly if they wash their hair in the bath.
Shampoos vary from being mildly acidic to mildly alkaline.
The cheaper shampoos tend to contain higher concentrations of the (cheaper) ingredients that make them slightly alkaline. A pH balanced shampoo will have a pH of around 5.5.
If your hair is lacking moisture, washing with an alkaline shampoo will just lead to more breakage.