I've been looking for soemthing to store DVDs so I took it. I tried several cleaners to remove the rust, None worked. Then I thought about that toilet cleaner "The Works", which is some sort of acid, and it always removed rust from my toilet. I put a little drop of it on one part of the rust, and that rust came right off, and did not damage the finish. So I just soaked a paper towel with it, and set that towel across the whole rust stain, waited 10 minutes, and it took the rust right off.
I washed it several times with dish soap to remove all traces of the acid, and it looks good as new.
One word of caution. I wiped that towel across it and got some of that on my fingers. That stuff really burns on the skin. A little soap and water stopped the burning though, but if I ever do that again, I'll wear rubber gloves.