The NFL's science-free smear campaign

So apparently the NFL has decided that they cheaty cheater New England Cheatriots have been cheating again, deflating footballs during games in order to gain some sort of advantage.  There are several problems with their campaign of accusation, though:

1. In cold weather, footballs lose air pressure.  (This is a consequence of what is known as Guy-Lassac's law from physics.)
2. Nobody on the team will admit to having done this.
3. Apparently they have no videos showing this happening.
4. It's not clear who had an opportunity to do this.
5. At least nominally, the balls were in the custody of the game officials.