I'm somewhat surprised that MIT just took money from someone based on a notable fundraiser's nod to do so. My understanding would be that a some kind of financial department would handle an application from the donee citing a joint interest between them and the donor [0]. That department would then investigate the donor for any red flags or question marks. This news is still pretty fresh, so I think there will be an investigation as to how all of this came to be and we will find out if there was any oversight process and if so, whether or not that oversight process was short-circuited in any way.
I mean I probably had to go through more for each of my job interviews and any corresponding background checks. Furthermore, MIT probably assesses potential students more thoroughly than what happened in this account of the event.
[0] https://definitions.uslegal.com/d/donations/
> The person making the gift is called the donor and the person receiving the gift is called the donee.