'Properly managed' in this context means that cattle (or other animals) are allowed to overgraze discrete areas, and then moved on, and the grass is the given a long time to recover before the next assault.
This simulates what happens in the wild, as the herds move over the grasslands.
After over-grazing the grass-roots die but because of the mycorrhizae within them they do not rot (or only very slowly), and the carbon locked within the roots significantly out-weighs the carbon in the exhalations of the animals. This is demonstrable and measurable.
This probably does not apply in short-term highly fertilized leys because they fail to build up mycorrhizae.
When ruminants are fed cereal they apparently exhale less carbon per animal but there is no compensatory gain because modern cereal production involves huge carbon loss.
Graham Harvey explains all this in his excellent book, 'The Carbon Fields'. The guy you quote in your piece, Dr Frank Mitloehner, is just putting the standard industry line. That is where the profit lies after all.
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