The league isn't concerned about a totally equitable schedule. Due to scheduling conflict that is virtually impossible. First and foremost they want to maximize viewership, as they should. It is an entertainment industry. That is the primary goal as it should be.

Every year certain teams are going to get a short end of the stick and there is no way around it. Part of their formula is to attempt to keep that from happening to the same teams the following year. As for Monday games, if you want to play on Mondays put together a winning franchise. The same goes for all primetime games.

What you are misconstruing is that there is something wrong with bias. The NFL isn't some sacred institution where everyone gets a participation trophy. It is a multi-billion dollar industry in the business of selling entertainment for dollars. They have a bias to get the most popular teams and players into the most visible timeslots.

However, given that is a subject of the gambling industry a different bias is involved. Any sort of manipulation of outcomes would be impossible to hide. Look at your example of the referees in the NBA. That came to light. If there is more than one person involved it will get exposed when gambling is involved. The gambling regulators of each individual state have dedicated staffs that do nothing but ferret out any signs of manipulation in all sports that they provide betting on. The NFL is the largest of those sports. If there was any hint of impropriety involving outcomes it would be front page news immediately. It has happened many times in the past in other sports. Point shaving, throwing games, etc. They always come to light. Someone ALWAYS lets it leak.

As for the league wanting Brady to win, that didn't help the league whatsoever. They know the public was sick of Brady and Tampa is not one of the best broadcast draws in the league. Besides, Brady didn't even sign with the Bucs until the schedule was almost two months into the generation process.