Sometimes it is in Duke's best interests for Carolina to win.
An example.
1978.
A maximum of two teams from any conference can advance to the NCAAs in that period. The ACC Tournament winner gets the automatic bid. But in 1975 and 1976 the regular-season winner lost in the tournament but got the second bid. Regular-season winner almost certain to get one of two bids.
1978 regular season. Carolina finishes first at 9-3, Duke second at 8-4. Tar Heels almost certainly in the Big Dance.
ACC Tournament. Duke advances to title game. Carolina plays Wake Forest in the other semifinal.
Why wouldn't any Duke fan root for Wake?
Well, if Wake beats Carolina and then Duke in the title game then Wake and Carolina would get the two bids and Duke would go to the NIT.
But if North Carolina beats Wake and then beats Duke in the title game, Duke would be the runner-up in both the regular-season and the tournament and would almost certainly get the second NCAA bid.
We all know how it turned out. But Wake Forest led Duke by five at halftime of the ACC Tournament title game and Duke was heading for the NIT had they not rallied.
So, sometimes heart has to take second place to mind and it is possible for Duke's best interests to be advanced by a Carolina win.