Many local officials on the U.S. side of the Rio Grande are panning Texas Gov. Rick Perry's latest initiative to stem illegal activity along the U.S.-Mexico border, complaining that the governor is wrongly painting their region as a lawless no man's land.

Last week, Mr. Perry said he is sending special teams of Texas Rangers to the border because of "the federal government's ongoing failure to adequately secure our international border." The Rangers, a state force that dates back to the 19th century, will focus on remote areas...