I have friend who is an avid collector of Native art and has a keen interest in the Native American culture.
When discussing the topic once, he pointed out to me a bow-and-arrow set, made by a Native American in the late 1800s, with a tassel on the bow carrying four beads of four different colors. They were each meant to stand for one of the peoples of the Americas. There was a black bead, a white bead, a yellow bead and a red bead. You can guess whom they were meant to represent. You see, the Natives see THEMSELVES in this way. They are the red people, and they have had pride in this probably for all of their history. They admire and look for the deep color of their skin and there's a reason why they disdain the 'pale' white man's look. They literally consider themselves red-skins, similar to how the ancient Sumerians referred to themselves as 'the black-headed people.' This is, at least, the historical truth.
And the story about how "redskin was used to describe Indian scalps used as bounties in New England" is a crock and has been proven to be so. Redskin is historically no more offensive than 'Fighting Irish' or other similar names, so you will have to re-arrange all of sports if you believe there is a problem, and you will be in fact disappointing many Indians who appreciate the pedestal and honor we have bestowed on them naming the Capital team of the country's flagship sport after them.