It is logical. Still, the American space program was founded by the former Nazi, and the Soviet Union, too, was so full of German experts (even anecdote on this subject is).
And it is not all-it matter was very funny movie (as I remember one of the three best comedies I've ever seen)!
Yes that is largely true. it may also be based on the Foo Fighters which Americans thought were German and Japanese (hence the creation of Steel Sky) and Vice-Versa.
there is also a minor Conspiracy stating that the Japanese had there own seperate Space Program or worked with the Germans on the same Program, which led to the inspiration for Steel Sky.