Just adding on:
1) I can't imagine that anybody checks the ball pressure during the game. So even if some balls were taken out of play out of concern they weren't properly inflated, can there really be any evidence that it was under 12.5 psi?
2) As I understand it, based on my rudimentary
science knowledge, the pressure of the air in a ball will decrease as the temperature of that air decreases. So if you inflate a ball to 12.5 psi and then check that air pressure inside (where I imagine the refs do it), then you bring that ball outside, then scientifically the expectation should be that the pressure of the ball will go below 12.5 psi once the air inside cools to match the temperature of the outdoor environment. This is in addition to whatever decreases in pressure might be caused by usage. Essentially, even if you measured the balls and found them below 12.5 psi during the game, that wouldn't be indicative of deflation or even a flaw in the ball. Its just indicative of science.
It seems like a situation where it will be impossible to prove any kind of wrongdoing by the Patriots short of a true smoking gun where they corner the ball attendant and he admits that, yes, the diabolical Ernie Adams payed him two grand to sneak the balls behind the stadium and let a little air out during halftime.