Army Maj. Stefan Cook sought out a notorious lawyer in February, formally volunteered for an Afghan deployment in May and was granted orders to deploy in June. But the Army reservist’s intention appeared not so much to fight for America as to fight against President Barack Obama, in furtherance of a bizarre conspiracy theory. In July, Cook filed a lawsuit against the Army, the defense secretary and the president, claiming that Obama could not lawfully order him to go to war because he is not the legitimate president of the United States. Cook is one of the so-called “Birthers,” a...