You're all sorta right. I worked at Singularity University for 2 years. They do 2 things:
1. Educate fabulously wealthy people in expensive executive programs
2. Use that money to put on a YC-esk incubator during the program where people come to build companies that use the technology of their sponsors. Google was one of the first sponsors. Peter Norvig was on the Faculty for a couple years. So was Astro Teller who heads their special projects (Google X).