I am reserving judgment and refraining from over-reacting until more facts come out (from the NFL), but I think the simplest conclusion is that the Pats fill the balls up to the level that they prefer by feel (without measuring psi with any gauge), hand them to the refs for approval, and the refs are in the habit of "rubber stamping" their approval. The Pats probably figure that if there are any issues, it's on the refs as arbiters of the game to ensure that the balls are in compliance. My guess is that many of the refs, who are full-time lawyers, accountants, salesmen, etc. during the work week distracted by other professional issues, don't test the footballs with any gauge and don't take this aspect of the job particularly seriously, probably because the league doesn't stress it. If the ball "feels right", it's good to go. They don't give much thought to inflation discrepancies, which explains why none of them had any issues despite handling the Pats' ball (no pun intended) all game without any issue. The refs' habitual inattention to compliance allows guys like Rodgers to play with overly-pumped balls, Brady to play with under-pumped balls, and who knows who else in the NFL to play with balls that are outside the 12.5 - 13.5 psi range.
If anything, this is the Pats (and Rodgers and who knows who else) taking advantage of lax compliance testing procedures. That's on the NFL.