It doesn't need to be a league-wide conspiracy.
If you're an NFL fan but not a Cowboys fan, chances are you HATE the Cowboys, right?
So if 10% of NFL fans are Cowboys fans, that means most of the other 90% HATE the Cowboys. Daily sports talk shows freely admit they rip the Cowboys after a loss because it draws big ratings.
Back to the refs...
If you're an NFL referee, chances are you were an NFL fan before becoming a referee.
Do the math. Most NFL referees probably grew up HATING the Cowboys.
Yes, their job is to be unbiased, but when it's a bang-bang 50/50 type of play that will decide a game, or a season?
Pretty easy to call it against the Cowboys and claim you were just doing your job, EVEN IF it's a subconscious bias against them.