Just to update with my actual experience in case anybody comes looking.

Asked at the counter - they said the same, it would be the fare difference. After about 10 mins they quoted me $6,000 (originally booked on a very expensive, fully refundable C). I think it had to do with the fact that I was booked on a UA ticket on the UA codeshare. I didn't press further because I didn't want to stand around, and also was afraid they'd reissue the ticket not on UA stock and I'd end up losing mileage accrual on UA.

Hope this helps.