Our law enforcement agencies have found bodies in the desert, either buried or just lying out there, that have been beheaded," Gov. Brewer said.
In Pima County, Sheriff Clarence Dupnik said not only is there no evidence of beheadings, but "the border is more secure now that it's ever been."
Murder? Burglaries? Rape? The major crimes? Up or down on the border?
"They're down," Dupnik said. "Violence in the cities is down."
According to the FBI, that's true across the southern border this decade. In San Diego violent crime is down 17 percent. In El Paso, Texas violent crime down 36 percent - it sits right across from Juarez, Mexico, one of the deadliest cities on earth. In Phoenix major crime has dropped 10 percent from 2000 to 2009.