I was browsing /r/gradadmissions as I've got a handful of interviews for rolling my MS over into a PhD lined up in the next few months and someone asked about something I had never considered before.
https://www.reddit.com/r/gradadmissions/comments/40rp4p/interview_times_are_upon_us_those_who_have_gone/
I really hope this Gerstner Sloan-Kettering story is the exception.
I'll necro this. I had post 9/11 GI BIll while being funded by the university. To answer what I think is your question: Yes, you can double dip. The university cannot deduct your GI Bill payment from the funding that they give you.