I’ll start this with what is an inescapable fact – one that many on here will agree with (and some will violently dispute):
Under the current setup, there is no meaningful “Big Sky Championship” in football. The only thing that really matters is who gets the FCS auto-bid to the playoffs, by whatever arcane rules the BSC biggies use. Yes, that does mean that a “co-championship” is “mythical” for many people.
But that pisses off, and rightly so, a lot of fans … because it makes a lot of Griz football history (essentially) irrelevant. We have been Griz fans for over a quarter century, but our fandom is peripheral … through family = faculty links, rather than actual alumni status. But for truly connected, old-time die-hard fans, it must be frustrating to crown a “champion” that played none, or only one or two, of the best other teams. And comparing those honors to a championship earned when every contender played every other contender … is just wrong. And we sympathize.
But that is also reality. The Big Sky, like the other really big conferences, is just a conglomerate of schools assembled for scheduling convenience. Win enough games -- whatever they may be -- and you get into the playoffs. Play and win against a tough schedule and, as “lobster” points out, you might get a top seed. The “championship” is a minor trinket you get on the way to the “real” prize.
If it’s any consolation, the FBS is pretty much the same, even when they are allowed a “conference championship” game. The top teams in the SEC (for example) may pay lip service to their “championship,” but their real goal is the FBS playoff or a “glamor” bowl game. Teams in the non-P5 conferences may value the championship a bit more, but they are also striving for a prestige, big-money bowl.
As to the strength of schedule (or lack thereof): Irrelevant … not because of the Big Sky structure, but because of the NCAA selection process. Really, really crappy conferences like the NEC, Patriot, Pioneer, etc. get auto-bids, despite the fact that they are largely non-competitive. Basically those are participation ribbons … validated by the (very) occasional upset in the first round. When weak BSC teams get auto-bids and are blown out … Does it really matter? Only to the fans of that team. Also ... Get away from “regionalization” in the early playoffs, and even “weak” BSC teams might make it out of the first round.