Can adding livestock reverse the desertification?

Allan pointed out a very unique way to fight desertification in his TED talk about reversing desertification. It is called planned grazing and holistic management. This way was done by increasing cattle and goats to form a livestock mimicking nature

Actually, many ecologists and scientists have tried many different ways to figure out how to reverse desertification and what is the reason causing desertification. But they have never understood. They have tried to remove battles to mitigate overstocking, but it turned out to be worse.To help grassland and biological decay, they also burned grassland to make it decay, but it causes more pollutants. Therefore, Allan pointed out the only option is making livestock mimicking nature. Why livestock make reversing desertification? I reviewed an interview of Allan Savory by Robert Blasiak. Here is the link http://ourworld.unu.edu/en/reversing-desertification-with-livestock/ 
Allan clearly explained why livestock is the main driver in this process, "The dead material will easy to shift from local rapid biological decay to gradual breakdown from oxidation in the condition of absence of adequate grazing herbivores. As a result, the dead material can filter  and inhibit the light from reaching growth points, and provoking the death of many grass plants."

Actually, Allan's work made a good result and many lands turn to be green again.

However, does the picture difference between 30 years is a good proof of real change? Is that kind of lack of science? There could be many reasons like the change of land and weather.
Without scientific testing, we cannot simply conclude that more livestock will be better than less.
I also review a blog from Berkeley, http://mdp.berkeley.edu/?p=568 relating to the concerning about feasibility of Allan's way.
Furthermore, do the adding cows fit for all desertification lands? Most people thought overstocking cause the desertification, is that totally wrong? If the lands have been totally deserted, feeding for the livestock will be a large process and how could this way solve the big land desertification?
I think Allan's way does work out some problems and help to mitigate the desertification, but the feasibility and long term result are still being questioned.