I don’t understand how this method is supposed to fix carbon sustainably. Microbe respiration on biomass is at least natural if not necessary. Even burning has long-term fixation benefits. Seems like playing short-term games with surface carbon, when clearly the long-term problem is total surface carbon.
I, as a layperson, can't say how legitimate this exact strategy is but, as I understand it the proposal is to change farming practices so that the soil's carbon content rises from ~1% to ~3%, reducing the atmospheric carbon content by an amount equivalent to what is added to the soil.
After that is achieved, no more carbon is removed from the atmosphere and what carbon was removed will only remain sequestered as long as the new agricultural practices are continued.
However, the claim is that this one-time sequestration of carbon is equivalent to humanity's last 150 years of emissions. I'd say that drastically improves our odds of migrating our civilization to sustainable practices in time to stave off all the climate-change-related catastrophes we would like to avoid.