The case is the Oglala Lakota Delegation of the Black Hills Sioux Nation Treaty Council v. United States, (D AZ, filed 11/2/2009) and relies on the language of the treaty stating:
Ray is the bad man among the whites, they argue. Many would agree with that proposition. The question is whether Ray can self-help himself out of a treaty-based prosecution.
This could make for some interesting litigation. One does not often see prosecutions of people who are defined as “bad men among the whites” in federal court. More importantly, the claim that a sweat lodge is the property of the Lakotas is meritless in my view and would raise serious constitutional questions. Yet, they insist that the Oinikaga sweat lodge ceremony is part of the Lakota’s oral tradition which, according to the United Nations Declaration of Rights of Indigenous Peoples, Art. 31, is protected.
This doesn't affect Turley's presentation, but it may raise an issue of standing in the courts. Can a delegation claim ownership of a ceremony when the relevant tribe or tribes haven't joined the suit?
I agree that this lawsuit has little chance of going far. It may have value as a PR effort: to raise awareness of treaty rights and cultural appropriation issues.
For more on the subject, see Ray Suspends Money-Grubbing, Native Scorn Ray's Sweat Lodge, and Suing the Sweat Lodge Killer.