Strangely enough I think it is because they are fundamentally disciplined and almost always commit fewer infractions than the team they are playing. The average low IQ fan (and announcer) expects to see an even number of calls to both teams not realizing some teams simply commit many more penalties than others....thus the "NE gets special treatment" myth is born.
Combine this with NE's success and what you get is tons of fan complaints to the league office from the legion of haters, and many officials who start trying to "even things up". Once an official starts down that road they are useless because they no longer reflexively just call what they see, they process calls through their higher mind that is trying to keep it even. When you get an imbalance of games actually decided by these bad calls it even makes it worse as they try to correct past blunders.
Thus..NE gets very contrived and awkward officiating.