I think people are confusing two issues. I know I'm confused. The problem to me is the amount of air in the footballs. I seriously don't know the scientific answers to these questions.
Does just releasing air from the football cause the PSI to go down? Or is it some other measurement?
Can the pressure go down without any air leaking, just from the change in temperature?
What Belichick was describing sounded like there was still the same amount of air in the balls but the pressure was just elevated do to vigorous rubbing(I know). Once it settled, the pressure went down, but the balls didn't noticeably deflate. Is that possible?
You and I both know the best to get air out a ball--poke a hole in it.
But normally, by far the best way to get the air pressure (psi...pounds/square inch) is to take a ball needle and let the air out. That will do it every time and that is how teams do it each week.
Next in line is put the ball out in the cold. It will eventually decrease the psi every single time. Colder temp allows the air molecules to get closer together. You can use water as an example---ice takes up less space than water, water less space than steam, etc. But it only decreases enough to equalize to the air temp, then it stops.
Another way, would be to sit something very heavy on the ball, but that enters into the integrity of the ball itself--and really, that is what the Wilson company wants everyone to know (truthfully) is not an issue.
The marketing dude from Wilson who said cooler air temp would not cause a drop in psi was flat out wrong. They developed the balls years ago, so there's no reason to have the developer from 70 years ago on staff. But you can be sure he would tell the representative to shut up. Losing psi due to colder air does not mean the product is flawed. It means we live in the real world where natural laws of physics apply .
In the end...
most would fairly assume (but not know for sure) that the MOST LIKELY reason a football would loose air is because someone took it our the normal way--with an air needle.