I was a perfectionist who worried constantly about my grades while I was growing up -- my own obsession was that I wasn't really as smart as other people thought, and that I was always on the brink of being found out. So anything other than a very high grade was sort of the beginning of the end, from my point of view! Financially, I felt a lot of pressure to do well, also, as I knew that I would have to get lots of scholarships if I wanted access to higher education. I used to plan that if I had kids, I would make sure that I had enough money that they could get all C's all the time if they wanted to!
Probe a bit with your daughter if you can -- how does she feel about her accomplishments? Does she believe she deserves them, or does she think that other people are mistaken in their high regard of her? Does she worry about letting people down, or losing what other people see as special about her? Maybe if you can get some answers about what is behind her upset, you can brainstorm how to deal with the (admittedly stupid) grading process.
If she enjoys the learning process but finds that it gets overshadowed by grade anxiety, are there alternatives within your school system? For example, alternative programs that offer more independent study opportunities and anecdotal report cards are available in many areas, and can be a breath of fresh air for bright, self-motivated students.