I know I said I'd wait until the new year to post what I think the other diversity jurisdiction issue is in this case, but upon reflection Alex's comments have set the stage for the answer, even if he hasn't given it precisely. Thus, I declare him the winner and provide my answer.
A hint comes from that source of all sources, Wikipedia (more specifically, from a paragraph in the concise but reasonably accurate entry on diversity jurisdiction):
Usually, in order for diversity jurisdiction to apply, none of the plaintiffs in a case can be from the same state as any of the defendants (complete diversity). . . . Cities and towns (incorporated municipalities) are also treated as citizens of the states in which they are located, but states themselves are not considered citizens for the purpose of diversity.
A state is not a "citizen" under the diversity jurisdiction statute. The presence of any state in a suit, plaintiff or defendant, destroys the diversity of parties. (That's the "you'll kick yourself" part.)
But, one may object, "this suit isn't styled State of West Virginia v. Richard Rodriguez; the Board of Trustees for WVU is the plaintiff!" That is true, and it raises the question of whether WVU should be treated more like a city (which is a citizen, normally) or the State of West Virginia itself. That is the issue I was referencing.
So, just for kicks and giggles, how would a federal court resolve that issue? I'll let (now former) Judge Luttig explain:
Section 1441 of Title 28 provides that "any civil action brought in a State court of which the district courts of the United States have original jurisdiction, may be removed by the defendant or the defendants, to the district court of the United States for the district and division
embracing the place where such action is pending." 28 U.S.C.A.§ 1441(a) (West 1994). . . . States, however, are not "citizens of a state" for purposes of § 1332(a). Moor v. Alameda County, 411 U.S. 693, 717 (1973). In addition, public entities and political subdivisions, such as municipalities, are also not "citizens of a state" if they are an
"arm or alter ego of the State." Id. at 717-18.
Maryland Stadium Authority v. Ellerbe Becket Inc., No.04-1743 (4th Cir. 2005).
Does the alter ego doctrine apply here? Well, in Maryland Stadium Authority the court concluded that the University of Maryland was merely an arm of the State of Maryland and ordered the suit dismissed for lack of subject-matter jurisdiction. From the discussion in the case, that result seems consistent with what other circuits have decided about other universities. However, it may be too much to say that there is a general rule that public universities are alter egos, even in the Fourth Circuit: Judge Luttig qualified his opinion by writing that alter ego determinations are fact-specific, and the panel came to its conclusion using a multi-factor test. Thus, there may be some hope for TRB's lawyers yet on the issue.
Alex will receive some low-value prize, probably from my collection of never-read or read-once books (my spare copy of Aristotle's The Nicomachean Ethics, perhaps), when I get around to it.
(And, yes, I know my cites are formatted incorrectly; fortunately, this is a blog, not federal district court.)