Though I haven't had this particular experience, I agree with peachfront. I'd definitely pay the full statement balance, and just leave the negative balance. There isn't really much harm I can think of that would result from leaving it there. If they don't send you a check for the difference, you can use the card later when you're not working on a minimum spend.

I think I've read about Citibank doing this (though I may be mistaken and it was really another card/bank). Maybe read around this forum and on the threads about the Citi AA card.