You sound pretty sure about that, and I might buy it but for one small problem - neither Brady nor Belichek said that was what happened. In fact, both of them, despite being pretty astute individuals familiar with footballs, pretty much said they had no idea what caused the footballs to deflate.
Other problem with your theory is that pretty much nobody else in the pro football world (mostly former QBs and players) is saying that is what must have happened either.
It would be a nice job if indeed it was the explanation, but it doesn't seem to be based on what those involved are saying.
First of all, I couldn't give two schicks what anybody else in pro football thinks. This isn't a theory. It is a physical fact. Don't believe me? Conduct your own experiment. Inflate a football to 12.5 pounds at room temperature, put it in the refrigerator for an hour (most refrigerators regulate temperature at about 37 degrees, roughly the same air temperature as the game that day), remove the football, and measure the pressure. The ideal gas law is a physical law that WILL apply to your experiment. The ball will measure somewhere between 10.5 and 11 pounds. Nothing the so-called pro football experts can say will change the immutable laws of physics.
Second, given the prevailing attitude and stunning lack of understanding on the subject, there is no way Tom Brady is going to tell the truth. I mean, we're talking explaining the ideal gas law to a thousand media hacks who didn't pay attention in 9th grade science. They'd crucify him.
And besides, It just doesn't matter. The rule doesn't account for temperature, so if the balls the Patriots turned in to the refs 2 hours and 15 minutes before the game were inflated to at least 12.5 pounds, then they did nothing wrong ... even if they knew the pressure would drop. They followed the rule as written. Again, if you don't like the Pats taking advantage of a rule, write a better rule.