The only sport I really follow is Football and my favorite team, the Redskins, has a well-known rival in the Cowboys. But the thing is, the rivalry only has meaning in the context of fair competition. I don’t actually HATE the Cowboys, at least not in the way I hate the Patriots and Seahawks (largely due to their unfair competitive practices). But in the end, the whole point of sport is supposed to be figuring out which team, or in the case of individual sports which athlete, is the best when competing as fairly and honestly as possible. As such, even if I might get a level of satisfaction out of seeing a rival miss the title, I wouldn’t want them to get it through dishonest competition, particularly if that is on the part of my favorite team. It also means that the team that DID win it might not really deserve it, which ultimately hurts ALL the teams by devaluing the championship.
So, no, I want to see my team compete as best they can, even if them winning helps a competitor or hurts their own draft position or whatnot. And in the rare cases where teams get advantages for doing anything less than their best, the rules should be looked at to not create a counter-incentive to honest competition.