Such as, there were three brothers who came over on a ship from England/Scotland/Ireland in the 1700s and got off at different cities. All of the (whatever surname) in America can be traced back to the three brothers. I have seen this story dozens of times.
Another one; he cleared a homestead in North Carolina, Georgia or Alabama in 1820 and married the daughter of Chief "About to be move to Oklahoma." She was an Indian Princess but took on the manners and dress of a white woman.
The last one, having Indian blood in the family tree is a strange one for me. I can't imagine any of my grandparents ever claiming to be part Indian, Native American, Cherokee or Seminole. Growing up in the South, having any connection to a minority group in the 1950s would have been very unusual. But today, many people claim to have a full blooded Native American great grandmother, or father when the reality is very different. In fact I haven't been able to document any family connection to Native American blood and have run down probably ten or more stories.
I had people on both sides of my grandmother Ila Rowell Green's family tree claiming that the other side was full blooded Cherokee. They even sent me photos to prove that this or the other ancestor was Indian. But they both claimed it for the other side. One side said Joseph Rowell was Cherokee and one side claimed it was his wife, Versanoy Smith.
In my research I have proof that neither were Native American. Joseph Rowell's father was William Rowell who came from South Carolina to Florida soon after it was sold to the US. He settled in what is now Taylor County Florida. Now some would say he had to be Indian. If so then he fooled a whole lot of people because he was chosen as a Captain in the Florida Militia during the Florida Indian Wars. He served several tours, very successfully driving the Indians south so the northern part of the State would be available to settlers. I found an old newspaper article about his military exploits at the University of Florida library.
So it must have been Versanoy who was passing as white, right? Well her father, Seth Smith was a well known Missionary Baptist minister and elder who founded the Missionary Baptist church in Taylor County. His father was a Methodist minister in Georgia. Pretty white bread on both sides.