<...I wonder how the US would react if the Mexicans started building villages in Arizona, and sent in their army to protect them. I suspect no US government could tolerate that.

You want to check and see how many citizens of Mexico are currently living illegally in Arizona, Texas, California, New Mexico, etc? The Mexican government doesn't HAVE to build settlements here. We build them, and Mexicans just sneak across the border and move in. Since most of them are poor and jobless, the Mexican government is tickled pink about this. There's more than one way to "occupy" a country. Of course, by the lights of some, that part of the country should still be Mexico anyway, so what's the difference?