They're both risky sports, but it's kinda like how the real Red Baron got shot down by AAA, not another fighter. Just seems wrong to go out that way.
The Red Baron was shot down by the American Automobile Association? *googles* Oh, wait.

AFAIK, anti-aircraft artillery was in its infancy during WW1, but Richtofen was shot down in April 1918, towards the end of the war. The anti-aircraft artillery generally credited with shooting down the Red Baron consisted of machine guns and possibly some light artillery, primarily used for ground-based defense. The technology was relatively primitive and not designed for anti-aircraft, so a ground-based machine gunner probably got lucky.