More like they don't want the wider public to know it was them that donated. Some folks that are extremely wealthy go to great lengths to keep their names out of people's minds and stay out of the public eye as a matter of personal security.
But to me that phrase kinda implies that the donor doesn't know who they donated to. Which…no. It should be blind to the recipient. Entirely blind. But people donating can still choose where to donate to.
Ah I see. I'm not sure that's technically possible, but if it were, that'd be great.
I think better would be simply outlawing any communication between a donor and recipient, if the donor wishes to officially remain anonymous. Not they "have no way" to prove their identity, but they're not allowed to prove it—or even imply it.
He might mean a certain specific group within the university. Ie the donor can donate to the University as a whole, but not say a specific branch of economics.