A VAT (as practiced in many EU counties) is a value add tax at every level of production.
the "fair" tax is only imposed at the moment of sale, like state sales tax is today. companies don't pay sales tax when they purchase component parts for their manufacturing. In a VAT tax, they do.
I know, that is just splitting hairs, but, really, the book is interesting, and most of these sorts of questions are discussed.
Whether it is "the answer" or not, its worth understanding what is being presented before you solidify your opinion of it.
I personally believe that, as presented in the book, it would be a significant improvement over what we deal with today.