My understanding is that this is not the case. A dozen years ago, I made a similar statement in an ecology class and the professor thought that the issue was important enough to ignore his planned material and spent half-an-hour raking me over the coals. The natives did burns, but their population was too small to have much of an impact. Lightning was by far the bigger contributer, but even so, burns aren't a long-term advantage. You would have seen a similar impact after grazing by sheep or goats as you did after the prescribed burn. In the long-term grazing is the better option.

Infact, ruminants and climate are what made the natural prairies. Lack of water favours grasses over trees. It's only in artificial prairies claimed from forest (ie. my farm) where one has to make an effort to keep the trees from taking the land back. But this effort is better made with livestock or a "brush-hog" than with fire. Rather than recycling nutrients into the soil, burning gassifies most of the nitrogen and potassium that would otherwise be incorporated into the soil. Enlightened farmers don't burn anything that they don't have to.

Here's the first link that "burning organic matter fertility" yielded on Google:

http://www.new-agri.co.uk/00-1/pov.html