If the NFL fixed a game then their would be issues in Las Vegas and DC because of the betting. beyond that, the damage done to their reputation would end the league.
Moreover there have been several politically-beneficial wins in the last 10 years -- the Patriots winning the Super Bowl after 911, the Saints winning it after Katrina, the Jets winning this year's Sunday night opener on the 10th anniversary of 911, in a metaphorical come-from-behind victory -- did you see how that game went down?
In the Jets game, Romo literally had to throw the game away in the 4th to lose it, and then his reputation was restored the next two weeks after two dramatic, media-hyped come-from-behind victories while playing with broken ribs and a punctured lung.
I've talked to many current and ex-NFL players at the gym and while the league has problems, fixing games is not one of them. When you're dealing at that level of talent small edges can mean big things. The emotional edge that one team has like in your examples can often push them to be just a bit better than other side. This is even more important when talking about a Super Bowl where both teams are evenly matched talent wise. In general the emotional/mental side of football is often way underrated.
Thing is, you show a couple of examples that are easily coincidences while there are many many counter examples. One big recent one is first super bowl in the new Texas stadium where the Cowboys were picked early season to go there and win. I don't even think they made the playoffs that year.
The NFL's lawyers stated the NFL competes in the "entertainment marketplace" (http://judiciary.senate.gov/hearings/testimony.cfm?renderfor...) and operates as a single entity, not as 32 teams.