It may not hurt them, but it certainly doesn't help them, especially when outreach programs, legislative initiatives, etc. come up. As a few have suggested, once the name/logo goes away the public awareness of the tribes and their "real" issues, such as poverty, crime, healthcare, etc., will diminish over time.
If the SR and SL tribes had any degree of pragmatism they would have used the Sioux name/logo as a "brand" or similar device to keep them in the public eye and give voice to their other concerns. If they were worried about "negative stereotypes", only being associated with "Dances With Wolves" or "F Troop" probably isn't going to help matters over time.