Funny, I had a professor in college who was probably one of the most educated men on Great Plains Indians and he actually says that is an untrue or coincidental story. According to him, Nadouessioux was a was used by the Algonquin translators the French which meant "those who don't speak Algonquin." So when they would introduce French explorers to new tribes, the ones off the great Lakes would get called Nadouessioux. The French shortened this word to Sioux and the name stuck.

You can see this mistake on old maps marking Indian families as some Sioux family bounds would suddenly be far off from the rest.