Hours after a battle in eastern Ukraine in August, a wounded and unarmed Russian soldier crawled through a nearly destroyed trench, seeking help from his captors, a unit of international volunteers led by an American. Caspar Grosse, a German medic in that unit, said he saw the soldier plead for medical attention in a mix of broken English and Russian. It was dusk. A team member looked for bandages. That is when, Mr. Grosse said, a fellow soldier hobbled over and fired his weapon into the...