Sure they can. They just gotta hire hire enough guards, same as if they were from Mexico City or Monterrey. You ought to read the history of that part of Mexico. In the mid 1800's the central government in Mexico was an ineffective joke and indios rose against the creoles (Mexicans of European ancestry). The creoles were driven off much of the land, and feared that they would be killed off entirely. They even offered to join the United States or become a colony of England or France in return for enough troops to suppress the peasants and give them their (under Mexican law) land back.
Some people think land belongs to them and just don't care that somebody else has a pice of paper that says different. (Think Ireland under the English where everybody on both sides was white to see this in a non racial context).
I repeat: know what you are doing before you wander the globe buying up land. You may get into a problem that you can't solve by saying "But I'm an American!"