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.