Beginning in 2000
Dilfer
Johnson
Eli (twice)
Flacco
are all tier 2, or lower, QBs who've won championships.
Brady
Roethlisberger
Peyton
are elite QBs who won at least one championship when their play was not yet (or any longer, in Peyton's case) elite.
Wilson
is a question mark as to where to place him.
The notion that you need an elite QB to win championships simply doesn't hold up to scrutiny. You need elite QBs to remain as a top contender year after year, because the truly elite QB can cover up a lot of team deficiencies, but Peyton Manning and Brady are the only two of those the league has seen drafted since 1998. And, for those who would argue Rodgers, that would still only make 3.