Fixed as in the way professional wrestling is? No.
But I do believe that the NFL has its preferred narratives/outcomes and probably takes an active hand in trying to sway things. In other words, they put their thumb on the scales.
I remember the Super Bowl that the Seahawks lost to the Steelers, there was the pre-game narrative of Jerome Bettis going back to his hometown and winning a Super Bowl in his last game. Great story, huh? And during the game, any time the Seahawks got some momentum going, the refs would absolutely fck them. That's just one demonstration.
And of course, there is Super Bowl 36, which needs no elaboration.
Basically, as long as games are close, the officials can sway the outcome. I don't think they do it every game, but I think they do it some games, and it's not beyond them to do it in a Super Bowl or the playoffs. I'm convinced we've actually seen it.
A lot of people won't want to believe it. But human beings are inherently prone to corruption, even moreso when they have power. Look at so many other big organizations - governments, large corporations, religions, charitable organizations - and you will find countless examples of corruption. Anyone who thinks that the NFL is immune to this is being naïve.
When you have a commissioner that routinely destroys evidence and have a league that has virtually zero transparency in its officiating, and yet still maintains its popularity, you have given the NFL and its commissioner a lot of power. Other than bad publicity, there really hasn't been any negative consequences for abusing their power.
So to summarize, while I don't believe the NFL actively and rigidly fixes games, I think they do actively try to influence the outcome of games and seasons. They are not always successful in doing so, but that rebounds to their benefit by giving the appearance of a level playing field, when there is anything but.