She didn't really go to Harvard
Chanel's personal website makes multiple references to her "Harvard" education. As it turns out, she actually attended the Harvard Extension School, not the university. While classes are taught on campus, often by Harvard professors, the extension school is pretty much open to the public. I guess that means that the old men playing chess in Washington Square Park can say they went to NYU, since they overhear classes taught by professors who want to be fun and take their lecture outside in the spring. Love that for everyone, to be honest, although I'm sure Chanel would consider public and affordable education way too communist.