Seems to me there is alot of private land on the border.
From what I've read, most the southern border is government owned.
There is. Most of it is populated with scrub-brush, Gila monsters, cacti, and scrawny cattle.
Much of the land surrounding the Corridor is privately owned. It cuts through the heart of the USA, from the southern border north to Canada, with numerous extensions out, to the east and the west. This is one reason why the 2006 Texas Republican Platform is against the Corridor: it allows for confiscation of private land.