What I've found on the issue is the open borders Libertarians talk abstractly about private property and freedom of movement, and do not acknowledge any Libertarian concept of free immigration with protected borders. Meanwhile, the rest of us are looking at the actual scoreboard of freedom, and have noticed we got more government force, more welfare state, less private property rights and less freedom of movement in the last several decades when more open borders immigration and amnesty policies/laws were adopted. Paul noticed too, and accordingly then developed a more complete libertarian approach to the issue.