but I wouldn't bet on it.
I'm not so sure that's a safe bet...consider the following.
In Virginia, the general standard for Group Libel is going to be somewhere around 25 people, with potential exceptions made depending on how the allegations are made. (In this case, "Jackie" impugned that Phi Kappa Psi, as a Fraternity was responsible for her rape, via the unchecked drinks, the incident that happened on their property alleged to be required for new pledges to take part (Directly implicating the Fraternity as an institution), and several of her attackers being of PKP Fraternity and supported by their fellow pledges)
One of the case law citations for determining an organization to be a private figure, capable of suing for Libel is Arctic Co., Ltd v Loudoun Times Mirror (Arctic Co. is specifically a front organization for the Iroquois Research Institute). Looking at an employment ad for the Iroquois Research Institute, we can see that they are an Equal Opportunity Employer/Affirmative Action Employer, indicating that, by the Federal government's guidelines, they have at least 50 employees, well over the typical benchmark of 25 members. To quote:
In addition to the basic EEO requirements, the regulations implementing Executive Order 11246 require supply and service contractors - generally, those with 50 or more employees and a contract of $50,000 or more - to develop and maintain a written affirmative action program (AAP).
Considering PKP is a Fraternity chapter on-campus of U of Va, I think it's perfectly reasonable to state that they depend upon financial support from the public, at least nominally in the form of support from the public university. If any part of their budget is made up of funds coming from the Uni budget, or grants provided by the Uni or State, that opens up the liability you just mentioned.
I think precedent would perfectly allow such a case to proceed, and, if it were to succeed that it would be an open-and-shut case.
I suppose the only way to truly test the theory, though, will be to see what happens if, and when, PKP presses charges against Erdely and Rolling Stone.