IMHO this has been a no-brainer all along. If the ball in inflated inside at a higher temperature (and rubbed up, which could in fact increase temperature even more), OF COURSE it will be deflated when it is taken out into the cold, this is not complicated and not controversial. I'm a professor of physics, but hardly the only one, you could call up probably 10,000 people (maybe way more) in the Boston area who know enough basic physics to uniformly reach the same conclusion (I published a link by BU Physics Dept. Prof. Martin Schmaltz several days ago on this). This result is not just possible, it is to be expected.
I think that BB called up one or more local physics professors and they said: "of course the pressure will decrease significantly if you rub it up inside and then later on take it out in the cold, and you can prove that it in a few hours with some simple experiments". But of course, the NFL should have already reached the same conclusions. But....no word from the NFL, in fact the noise about cheating and so forth was just getting louder.
So I think BB decided to have the Patriots do these simple experiments themselves (doubtlessly with the help of some local physicist) so that things didn't drag out any longer, to force the league to explain why they haven't performed that obvious step.
I admit that I'm a big Patriot Fan so maybe I'm not being as scientifically skeptical and rigorous as I would be in my work environment, but it seems to me that the NFL should have come to this obvious conclusion long before now, exonerating the Patriots. Why had that not happened? I would hope that will be the REAL scandal that comes out of this whole fiasco, but with Goodell as the scandal target. I think I heard a hint that something like this (a payback) may be forthcoming from the Patriots in BB's speech.