Early one evening in May 2012, an extraordinary hour-long radio conversation attracted the attention of various listeners among the NATO forces in the Afghan theater. On one end of the conversation were the pilots of two U.S. Air Force A-10 Thunderbolt II attack planes, who had been patrolling the eastern province of Paktia, not far from the Pakistani border. They were on call for any ground unit needing “close air support,” a task for which the A-10 was expressly designed.

On the other end was a Joint Terminal Attack Controller (JTAC), a specialist whose job is to assign and direct air strikes.…