I can guarantee you, if UK was the last team standing, there is no fan of a single SEC school, that will want to see UK win.
If Tennessee, Florida, Auburn, Arkansas, or Alabama was the last SEC team standing, it would come down to who they were playing. While I don't want them to win, if any of them are playing duke, unc, ucla, ku, or uconn, I will pull for the SEC team. That’s not conference honking, that’s just me not wanting the other blue bloods to have success.
Same with Louisville, they have fans that suffer from little brother syndrome, they will immediately shove it in the face of UK fans.
Everyone has a rooting interest and it's for different reasons, but for most people, it usually goes back to wanting their own team to look the best it can.