Hi Despair,
Generally speaking, the fellowship pays the university 2,000 dollars towards tuition with the understanding that the university waives the remainder of your tuition/fees. Most universities will, in fact, do that. (NSF fellowships give 10,000 towards tuition/fees, and universities waive the rest.) In regards to the stipend... where I'm going, it costs a LOT more to live there than 18,000 a year, so my program will supplement that stipend so that it's the same as it would be if I were using the university's stipend. Of course, it all depends on your financial package to begin with. Does that answer your question?