Rabbi tells the cop that he's Satchel's guardian because his father was killed by the Germans at the end of the war. While the US Army had been segregated during WWII, there were multiple possibilities for why the policeman (already sympathetic to their situation at this point) might have considered it plausible, including that Satchel's father could have been white.
Rabbi says Satchel's father was killed by the Germans on Armistice Day. That would have been the end of World War I, November 11, 1918, or the holiday celebrated on its anniversary. The end of hostilities with Germany in World War II was in May 1945 and was referred to as V-E (Victory in Europe) Day in the United States.