Agree in general, though Von Braun himself wasn't in the private sector. All of his work was sponsored by the Nazis directly. With all the nationalistic fanfare surrounding the moonshot, the man directly responsible for putting us there is an SS major, and the engines that got us there are directly descended from V-2.
It's true he pretty much came directly out of university into the Nazi party. He wasn't the only person responsible for NASA's success though. It took a lot of engineering talent from several different fields to make the Apollo program happen.