I think there’s a few different potential kinds of cheating:
1. Refs influencing games to keep them close so people don’t tune out. This one is plausible because blow-outs are pretty rare in the NFL relative to other football leagues. Teams always seem to make it a 1 or 2 score game in the final minutes, often helped along by big pass interference penalties. Block in the back penalties on kickoffs could help to hamper field position of teams in the lead to stifle momentum. Ticky-tacky or non-existent personal fouls on the defense, especially roughing the passer, frequently extend drives on big third day defensive plays. The methods are there to keep games close.

2. Officials influencing games to manipulate gambling outcomes. This has been shown to happen in other sports. Why is it so illogical that it could happen in football where a garbage time TD could decide the fate of millions and millions of dollars?

3. League officials showing favoritism to teams for ratings. This is a common allegation by small market teams. Many assume that large market teams draw better ratings, thus the league should want big games involving competitive big market teams, right? In addition, if the league is really seeking to maximize ratings, it should try to ensure the teams playing for the title don’t have overlapping fanbases to get as many eyes watching as possible. Leagues should desire big markets and geographic diversity in their title matches. So, having Los Angeles vs Boston is a much more lucrative matchup than New Orleans vs Kansas City. However, I don’t think there’s enough evidence of this being a primary factor.

4. League officials rig outcomes via favoritism towards certain owners aligned with the commissioner’s agenda. There have been a lot of allegations of favoritism regarding the relationship between NFL Commissioner Roger Goodell and New England Patriots owner Robert Kraft. New England vastly outranks all other programs in receiving compensation picks and received comparatively light penalties for various cheating scandals and off-field shenanigans over the years. By comparison, the Saints program was absolutely rocked by Bounty Gate penalties even with almost zero evidence, and the Saints are dead last in receiving compensatory picks. Saints officials were also vocal in opposing the “findings” of the NFL and attempting to criticize the NFL’s officiating and decision-making. Some believe that behavior made them a target for rigging against them. Some teams seem to consistently have players suspended for longer periods and at more critical times than other teams. This control wielded by the Commissioner gives him a lot of power to influence the number of draft selections for a team as well as the number of players available to individual teams on Sundays. That’s not enough power to completely change an outcome, but can have significant influence on a team’s overall talent and performance.

We don’t know if leagues are mass rigging games, rigging some games, point shaving, or showing favoritism, but they have the motive, they have the means, and they have the kinds of statistical anomalies and patterns that would suggest such behavior could be occurring.