This makes zero sense. Lack of a reliable closer isn't the reason neither of them has won a WS this decade. Hell, they've made the postseason several times between the two of them with elite closers without winning jack squat.
This, however, makes more sense, but is still misguided to an extent. The closer is important, yes, but having several go-to guys in the BP is even more important, as you present here. Even though he shat all over himself in the WS, the Sox don't even make it without Craig Breslow's and Brandon Workman's contributions, the unsung heroes of the post-season.
I was the "Koji-for-closer" club's leader all season long, so it's not like i'm discounting his dominance. He would have been just as important, however, in a relief-ace role instead of the annointed "closer" tag based on an archaic, nearly-meaningless stat.