Many / most schools admit people with no diploma on the basis of their work. This is why many students apply as Juniors in high school and how early admission works. If universities required a high school diploma as a qualification, students wouldn't be able to apply until they actually completed high school. There are many cases of people entering college as early as 13 years old, and this is not limited to MIT.
Early admission has nothing to do with having a diploma. All undergraduate and graduate programs let you apply before you have finished the previous level because the application and acceptance process takes more than the time between schools.
In cases where diplomas are required, the acceptance letter will always contain language stating that they will retract your acceptance if your grades drop an unacceptable amount or you don't finish the degree you're working on. Then most schools require you to submit another set of transcripts, proof of graduation, etc. before you officially enroll.
of course you don't have the degree when you apply and get accepted. the whole point was the guy didn't have a high school to go to, wouldn't ever get a degree, and MIT was awesome enough not to care.
There were freshmen as young as 15 when I was at MIT, but as I remember it, they generally had graduated from high school. It's not that unusual to be 17 when you start college, so if you've skipped a year or two you could easily be 15 when you get to MIT (and generally, it's also fairly possible to take some extra classes and finish high school a year or two early.)
