I really don't think the game(s) are fixed in any way.
I think it's very hard to subtlety influence a one-and-done playoff format to try and create what you want from a league perspective. I think the randomness and variety of penalties and odd things over the years is just normal statistical variations.
Of all the sports, the NFL is least effected by "big market" forces. People watch the Super Bowl no matter if Indianapolis, Seattle, Pittsburgh or New York is playing. And the add revenue is "fixed" way before the teams are decided.
I just see no good statistical evidence that the league favors any one team over another.
Not all of us, the last super bowl I watched had the steelers playing in it, when they are done so am I.