Its very simple. Miami grew up as an independent so the older fans, and most younger, dont identify with any conference. After all, we did it without them and we've been in two conferences within the last 20 years. If we had been in the ACC from the 1930's, we all would have a conference mentality because it is of utmost important to win your conference. We got in the big bowls by being a very good team people could not ignore, same for PSU back in the day. But in the conferences, you could not go to the Cotton Bowl (SWC), Orange Bowl (Big 8), or the Sugar (SEC) unless you won your conference. If your conference was good, you could sneak into a big bowl game by having a strong conference and having the reputation of traveling well. That mentality has been ingrained in the old guard, SEC, Big 10, old Big Eight, whatever for decades.
What is important now, is that we recognize that we must find a way to the conference championship game first, hopefully the conference isn't full of retards that lose to DivII (orwhatevertheycallthemselvesthesedays), win the conference title game, and hopefully that punches our ticket to, at worst, the OB, and next year and beyond worth a top 4 tourney bid.
Whether we like our rivals or not, its in our best interest that anyone on our schedule win as much as possible. And we need a strong conference regardless of schedule.