In my experience this isn't uncommon. I had a friend a few years back who didn't apply to graduate school at all but applied for the NSF GRFP, was awarded, and had to scramble at the last minute to find programs that would admit them in the fall. Why they didn't apply for graduate school in the first place isn't clear to me, but I think it had to do with personal reasons. I know people who were able to do this without the NSF (but that's much harder and requires a lot of finessing). Basically for me, there was a program I really liked but didn't apply to (didn't find out about it until after the deadline), so when I got the NSF I decided to reach out on a limb, worst they could say was no. I e-mailed them, said hey I have my own funding, here's my application materials that I sent to similar programs, I'm really interested in your research, are you interested? And based off that e-mail alone I got a Skype interview and I'm flying up next week for an in-person interview. I've spoken to many professors at various universities who have all stated that if a professor really wants a student and that student has secured funding, it's not difficult for them to convince the graduate school/ department to override the application process and let the student in. Obviously it's an unconventional scenario, but it happens.