I posted this elsewhere:
The ref thing is essentially a perception issue, so I think the league should invest in an independent study of all game video for a substantial random sample of games. All missed calls that were not made and all calls made should be tallied and the numbers should be released to the public.
This needs to be done so that the league can say, "look, refs will never be perfect, but here are the numbers and we can see that the missed calls even out". Without doing this, we are leaving the evaluation to casual viewers who don't know how to evaluate this scientifically and who don't have the research savvy to control for their own biases.
Of course, even if such a study were to be done, let's be honest. Many fans won't have the mathematical sophistication to actually understand it. They would still prefer anecdote to a scientific study. I don't think there is any reason to think that conspiracy theorists are interested in scientific studies.
The study would be particularly interesting if it included an analysis of what plays are hardest to get correct, and what styles of play most benefit from limitations of referees.