You are more or less right, but since the process occurred on a state-by-state basis, and over decades, there are lots of exceptions and variation. They actually were not "administered" by the states, but deeded to them. In many places, they have been sold or traded to create meaningful blocks. In some states, when they are leased to ranchers, all other uses and access become controlled by the rancher and they become functionally indistinguishable from private land.
