I've been a lurker here for a long time but never had any need to comment because you all cover it far more adequately than I do. This brouhaha has me wanting to weigh in and I apologize for being insufficiently erudite compared to the football minds that populate this forum.
I assume the Rulebook on NFL.com is complete and this feedback is based on that.
The rules say that a football has to be 'inflated'. No mention is made as to what it has to be inflated with or what the temperature of the gas used to inflate the ball has to be. I am no chemist or physicist but it seems to me that various gases at various temperatures could be used to inflate the ball in order to allow the ball to pass inspection 135 minutes prior to game time but to slowly lose pressure as the gas cooled and/or the outside temperature dropped. The addition of water vapor to a heated gas could also allow for a ball to pass inspection but over the intervening 135 minutes the water vapor would condense as the gas cooled, thus lowering the PSI. Similarly, I do not know what the permeability of urethane (the bladder material) is but might it not be possible that some of the smaller gases like hydrogen or helium would slowly seep through the urethane lining, especially if heated gas is used which would expand the urethane and presumably the porosity of the bladder as a result of expansion due to heating? Again, no scientist here, just using what I recall from basic sciences.
If the Patriots (or TB acting on his own) had a roll in Deflate-Gate or Ballghazi or whatever nonsense name one wishes to assign to this story, I would fully expect them to have a reference matrix of temperatures, barometers and weather conditions in order to get the ball to their desired PSI by game time. It's on the refs to detect any problems with the pressure of the ball after they pass initial inspection because the balls are out of the team's hands by then. Any suggestion that the Pats would leave this in the hands of a ball attendant on the sideline is preposterous.
Like the exchange from De Niro to Pacino in the movie Heat: "I do what I do best, I take scores. You do what you do best, try to stop guys like me."