Lessig's theory of anonymous donations seems to have been carefully developed for the sole purpose of exonerating Ito, who is Lessig's friend. It's not like there's some new revelation that's come out since Lessig wrote his piece.

I think no theory of anonymity works. A villain isn't going to keep their pinky-promise to not tell everyone that your prestigious institution took their money.

It’s not particularly difficult to make a donation anonymous in a way that the recipient genuinely doesn’t know who made the donation. Just have a neutral third party handle it. This could be a donor advised fund or a trustee, for example. I suspect this isn’t particularly rare.

But then the donor tells the recipient that they are the ones who donated all of that money. And so they get all of the benefits anyway.

I just gave you $10M. Can I have a private dinner?

Do you believe me? If an anonymous donation is done with some degree of care, you have no way to verify my claim.

If a $10M anonymous donation had just showed up in my account and I hadn't told anyone, then yes I would be inclined to believe you.

That would be part of handling anonymous donations sensibly. The transaction should be between the development office and whatever trustee or foundation gives the gift. The ultimate beneficiary shouldn’t be notified of the donation until, say, the end of the fiscal year, at which point all anonymous donations are aggregated.