Naturalization is one, yes.
Also, I think it depends on what your definition of "invasion" is as to whether open borders are Constitutionally preferred.
Article IV, Section 4
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
A court could hold such definition to be similar to an invasive species of plants, which is non-native to the area (I don't have time to look up whether any court decisions have validated this line of thinking, which is held by many who favor a strict immigration process).
I also think the "freedom of movement" has been held by the courts to mean that you can travel from state to state or city to city within the U.S. without papers, not country to country.