who really won the men's 100 meter freestyle

Ferenc Csík, a Hungarian. I wonder if there was any reason his contest was the one featured in the movie.

It would have been remarkable if he had survived WWII and its aftermath, the Nazis, the Allies, and the Communists. It was a lose/lose situation for them. It would be interesting to know how many of the Hungarian team in the 1956 Melbourne Games remembered his name. The Soviets crushed the revolution in Hungary as the athletes were en route to Australia. The water polo team went up against the Soviet Union team comprised of military personnel. The Hungarians won. There was blood in the water and the authorities looked the other way when it was the Soviets who were the ones bleeding. One might say it was the closest the Olympics ever came to warfare.

From Wikipedia

Ferenc Csik (12 December 1913 – 29 March 1945) was a Hungarian swimmer who competed in the 1936 Summer Olympics.
In the 1936, Olympics he won a gold medal in the 100 m freestyle event and a bronze medal in the 4×200 m freestyle relay event. Csik went on to become a medical doctor, and died during World War II in an air raid while assisting a wounded man.[1]
See also
World record progression 4 × 100 metres freestyle relay
References
Wallechinsky, David (2004). The Complete Book of the Summer Olympics, Toronto: Sport Classic Books. ISBN 1-894963-34-2

One might also say that using the Olympics as the setting for a movie in a time when war seemed to be in the air, the message was of coming together in a peaceful way to solve our problems although that looked increasingly unlikely. One might suggest that showing Jesse Owens winning and a Chinese man doing better than the German police in a mutually respectful manner while another beats the competition in the swimming event with no regard to his ethnicity was a response to the bigots in the US as well as Germany. After all, Chan probably wouldn't have been married if he hadn't been living in Hawaii rather than the mainland US, and any hint that his son would have been able to romance one of the White members of the Olympic team would have been horrifying in parts of the US at that time. Audiences might have noticed other things than Hitler in this movie, and that might have been the reason the Nazi symbolism was not the focus, and in fact was out of focus. It wasn't just the Nazis who were in favor of White Supremacy in that era, or any era.