I don't think the league is rigged. Do I believe Goodell has biases? Yes. Do I believe the refs have biases? Yes. After all they are only human like the rest of us. But I do not think the league is acting to get one team or another to the Super Bowl. If evidence came out that the league was rigged, I would hope the league or congress, would act to clean it up and penalize all those who rigged it. I would stay a Cowboys fan though the cleanup. But I would sue or encourage a class action lawsuit against the NFL for a return of all the money I paid for NFL ticket when I was a subscriber.
Having said that, the league has an officiating problem. The refs are awful and everyone sees it. I think the problem is not just part time refs. It is part time refs with complicated rules that leave a lot of calls to the judgement of the refs.
IMO, they need to go through the rulebook and look to rewrite the rules so that refs have an easier time calling penalties or letting them play.
Let's take pass interference and illegal contact, for example. They can change the rule to make any intentional contact past 5 yards illegal and a 5 yard penalty. If the ball is in the air, whether it is catchable or not, it becomes PI.
Offensive holding can be changed to allow grabbing as long as the arms are not wrapped about the defender. We see them let this go most of the time anyway. It is silly to say that grabbing a guy in front of you inside the shoulders is okay (even though the rules says its not really), but if he doesn't let go when the guy changes direction then it's holding. The whole point of grabbing the rusher by the pads is to keep him in front of you and materially restrict his path.
I am not saying I advocate for these changes. I am saying that asking part time refs to make judgement calls leads to mistakes, and inconsistency around the league. It is the inconsistency that people really react to.