Tribal corporations are still sovereigns, end of story. From United States v. Bly (concurring opinion)

It does point to the fact that, in addition to being a state agency, the University is a corporation under state law. This is true but irrelevant. The Supreme Court has never suggested that the state law designation of a sovereign entity as a corporation eliminates that entity’s status as a sovereign. Indeed, when a sovereign Indian Tribe and a corporation that was an “ ‘arm’ of the Tribe” sought to be recognized as “person[s]” under a federal statute, the Supreme Court denied this status to both the Tribe and corporation, without distinguishing the two, because both were sovereign entities. Inyo County v. Paiute-Shoshone Indians, 538 U.S. 701, 704, 705 n. 1 (2003). Similarly, the Court has recognized that although “state officials literally are persons,” they are nonetheless presumed not to be included within the statutory term “person” when acting in their “official capacity” because in those circumstances they are “no different from … the State itself.” See Will v. Mich. Dept. of State Police, 491 U.S. 58, 64, 71 (1989).