LOGAR PROVINCE, Afghanistan — Staff Sgt. Marcus Jimenez was pissed. On March 19, he had led a force of U.S., Afghan and Jordanian soldiers into the village of Pakhab-e’Shana, in eastern Afghanistan, with what Jimenez considered the best of intentions.

While the Americans conferred with village elders, the Jordanians and Afghans would inspect the town’s four mosques, to see if there were any repairs NATO and the Afghan government might help pay for. In addition, the Americans and Jordanians had some soccer balls to hand out.

But the elders greeted the soldiers with what looked like cool...