I think that any school would be so thrilled to win the championship that except for perhaps one circumstance, they would not attach an asterisk, mental or otherwise, to the accomplishment. I, for one, certainly don't diminish UConn's championship from last year just because Baylor wasn't the opponent. Baylor fans won't necessarily agree with this but their team lost fair and square last year. Their team was whole - no significant injuries that changed who they put on the floor. Notwithstanding the impact of referring in the Louisville game, I think almost everyone agrees that Mulkey was outcoached that night and that was the biggest factor in the upset. Coaching, good or bad, is just part of the game and is why I consider Baylor's loss fair and square.
The one possible exception is if a team has significant injuries so late in the season that they don't have time to adjust. I'm thinking UConn without Shea and Svetlana. I know that injuries are part of the game, just like bad coaching, but for me, this is a different kind of obstacle.