Are you sure about that? Pierre Trudeau served in Canadian Officers’ Training Corps from 1943 to 1945 in Montreal during World War II, but never deployed overseas.
I recall the story being discussed when he passed away in 2000 and also that a writer mentioned the irony of Dorval Airport in Montreal being renamed for him because it used to be an important aircraft facility for the Royal Canadian Air Force during that time and he did this little stunt to annoy the workers and servicemen there. He did indeed serve in the capacity that you mention though.