The 2007 New England Patriots were probably one of the best NFL teams of all time. They went undefeated all the way up until the Super Bowl, but were upset by the Giants. In many sports it doesn't matter how great a season you had, if you cannot be the best on that crucial day then sorry. Somehow those fans manage to carry on without whining about "legitimate" champions.
There are many differences, but one is that the NFL doesn't let all 32 teams on the field for the Super Bowl. To have your championship run ended by the actions of some guy in 30th place is fundamentally unfair. It'd be like if Peyton Manning had a TD pass batted away by some player coming off the sidelines for the Titans.