The doubts about the technique seems warranted. On the other hand there is a simple reason why it might be true : if large herds destroyed the herbs on which these herds depend on, they would die off. So from an evolutionary point of view, it makes a lot of sense for large herds to fertilize soil. They NEED grass to thrive.
There are few simple rules to count on. The stability of grasslands depends on circumstances, usually including a range of herbivores to prevent forestation. Mega-fauna, like mammoths used to contribute to grove and prairie creation by eating trees, before humans dominated.
I wrote this to dereke in another comment, I think it is relevant to understanding the present situation:
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Two hundred years ago about 60% of the earth surface was covered in mature and native forest. The figure is less than 30% today. Most of the worlds fertile crops are grown on deforested land, on the soil which native forests developed through ecological diversity and lack of erosion. Most of the grasslands which are used for grazing, don't have the soil quality to support demanding crops.
In particular, this Descartes quote
"I should like you to consider that these functions (including passion, memory, and imagination) follow from the mere arrangement of the machine’s organs every bit as naturally as the movements of a clock or other automaton follow from the arrangement of its counter-weights and wheels."
