I think you probably are not from the USA or you wouldn't refer to the Germans and Dutch as two different "races"; in American English we tend to reserve the term "race" for the "big four" White (Caucasian), Black, Asian, and Native American. The Dutch and Germans are two different nationalities. But the German word for "German" is Deutsch, and in the 1700s in North America this caused confusion. We have the term "Pennsylvania Dutch" in the USA, which refers to people of the Mennonite and Amish faiths in Pennsylvania who are of German descent; their ancestors did NOT come from the Netherlands. The term "Black Dutch" goes back to the 1700s, when it was common to refer to people from all parts of Germany and the Netherlands as "Dutch."
I have never heard the phrase "Blue Belly Dutch." The story you tell seems like a "folk etymology" to me; a story made up to explain a word or name after the fact.
If you look at the following link you will see that there are at least seven different groups of people in the USA who have been called "Black Dutch" at one time or another. (By the way, I do not agree with the theory on this site that people with black hair and dark complexions in southern Germany must be descended from Roman soldiers from Africa! I think black hair has always been one of the hair color variations in all European groups.)
http://www.geocities.com/mikenassau/BlackDutch.htm