Stephen Thompson was associated with a lot of American firsts. He flew as an observer in the First Aero Squadron, which was not only named "First" but really was first. The First Aero Squadron got its name by being the first squadron of aviators operating in the US Army, flying the first American aviation mission launched from American soil over a foreign country (i.e. Mexico, which is about 4 miles away from Columbus, New Mexico, where they launched from) to keep an eye on Pancho Villa for Pershing. Remember, Pancho Villa's attack on New Mexico was in its way worse than the Pearl Harbor attack. New Mexico wasn't just a territory, it was a state of the US - and had been that way for all of four years!
Stephen Thompson was not closely associated with that first mission. As far as I can find, Thompson was in college at the time, and his first association with the First Aero was in Europe. But once there, he got busy, and scored the first all-American aerial victory - that is, a victory by an American, under American command, after America was officially at war. (Kiffin Rockwell got the first victory by an American, but flying under French command at the time.) So his name got linked in history with the First Aero Squadron, and close in time to the First Aero's first mission.
As an American aviator who didn't fly for the French, Stephen Thompson was not part of the Lafayette Flying Corps, but as one of the earlier American aviators to get "over there" after the declaration of war, was closely associated with them.
One of the pilots he eventually got to know was Edwin "Ted" Parsons, one of the original Lafayette Escadrille pilots, who not only learned to fly before the war, but was flying in Mexico back in 1913. Pancho Villa wanted him to train his men, but apparently in the uncertainty between Mexico, Pancho Villa, and the US about who was the enemy, Ted Parsons decided he was not exactly on Villa's side, and left for Europe, never actually flying for Pancho Villa at the time the First Aero Squadron was flying against Villa. He also apparently never actually flew directly for the US in WWI (he did in WWII), staying in the French air force even after US forces arrived.
So Thompson and Parsons were both renowned American aviators who were never quite on the same side, and were associated with opposite sides in a previous conflict - except for the minor detail that neither was there at the time! We recently heard about this story from Andy Parks, who said Thompson and Parsons enjoyed kidding with each other about having been on the wrong side.
Our Lafayette Escadrille shirt is a good one to wear while telling the history of these "frenemies".