Stigler wasn't just motivated by vengeance that day. He also lived by a code. He could trace his family's ancestry to knights in 16th century Europe. He had once studied to be a priest.
A German pilot who spared the enemy, though, risked death in Nazi Germany. If someone reported him, he would be executed.
Yet Stigler could also hear the voice of his commanding officer, who once told him:
"You follow the rules of war for you -- not your enemy. You fight by rules to keep your humanity."
Alone with the crippled bomber, Stigler changed his mission. He nodded at the American pilot and began flying in formation so German anti-aircraft gunners on the ground wouldn't shoot down the slow-moving bomber. (The Luftwaffe had B-17s of its own, shot down and rebuilt for secret missions and training.) Stigler escorted the bomber over the North Sea and took one last look at the American pilot. Then he saluted him, peeled his fighter away and returned to Germany.
"Good luck," Stigler said to himself. "You're in God's hands."
What creates the bond between enemies?
Stigler was able to recognize the common humanity of the enemy when he locked eyes with Brown. It caused him to take mercy.
That sudden recognition can spring from many sources in battle -- hearing the moans of a wounded enemy; sharing a common language; or opening the wallet of an enemy and seeing pictures of his wife and children.
That respect for the enemy's humanity typically starts at the top, some scholars say. A leader sets the tone, and the troops get the message. A military leader who embodied this approach was one of Germany's greatest World War II commanders, Field Marshal Erwin Rommel, also known as the "Desert Fox."
One time, a group of British commandos tried to sneak behind enemy lines and assassinate Rommel in the North African desert. They failed. But Rommel insisted the commandos be buried in the same graveyard as the German soldiers who died defending him, says Steven Pressfield, author of "Killing Rommel."
There were battle zones during World War II where that type of magnanimity was almost impossible. On the Eastern Front, German and Russian soldiers literally hated one another. And in the South Pacific, U.S. Marines and Japanese soldiers took no prisoners.
At times, the terrain can force soldiers to follow the code. The North African desert during World War II was one such place, Pressfield says.
Fortunes turned quickly because so many battles were fought by fast-moving tanks and mobile units. A German unit that captured British soldiers could end up surrendering to them minutes later because the battle lines were so fluid. Also, the desert sun was so harsh that both sides knew if they left enemy prisoners stranded or mistreated, they would quickly die, Pressfield says.
It was not unusual for German and British doctors to work together while taking care of wounded soldiers from both sides, Pressfield says.
Some British and German soldiers never forgot how their enemy treated them and staged reunions after the war.
"The Germans and the British used to get together for soccer matches," Pressfield says. "It was the Desert Foxes versus the Desert Rats."
These soldiers weren't just engaging in nostalgia. They shared a sense of hardship. They had survived an ordeal that most people could not understand.
"In many ways, a soldier feels more of a bond with the enemy they're fighting than with the countrymen back home," Pressfield says. "The enemy they're fighting is equally risking death."
That bond could even lead to acts of loyalty after the war, says Daniel Rolph, author of "My Brother's Keepers."