Does the industry route count? Many people in private labs (Google, OpenAI, etc.) got there the private route without school. That was actually going to be my backup plan. In fact, one of the first authors on GPT-3 is now at Columbia working on her PhD somewhere down the hall. She's in year 3, so do the math... Now I know the true meaning of imposter syndrome.
My unclear interpretation of the rules was that when you apply for GRFP you must state an "intended school". It felt disingenuous to state a school I didn't apply to, ergo you should apply to a school. But I have no reason to believe it is verified in any way shape or form.
This is good advice. It is very helpful to 1) have a home school that will let you stick around as a backup and 2) have a sufficiently general research topic and flexibility to apply to make many schools be good fits.