I'm simply saying that the BE does indeed say that those NC's were achieved by a BE school and that the BE is still alive and kicking, as someone else says its more about trying to say that the BE never ceased to exist and is still the same conference. UConn owns their own championships and the BE simply says they were a member of that conference when they won them. Click on the media guide I linked it's all there. You are saying they have no right to claim whats in the media guide. With the amount of lawyers involved in the break, my guess is that you are incorrect.
To articulate this further, You say the Big East didn't exist before 2013 essentially. I ay the BE purchased the right to say they have always been there as they are now, which is exactly what they claim in all their published and posted materials.