My guess... the equipment manager used a football needle about the time the game started and let a little bit of air out of each ball. Until he could squeeze it about like Brady liked it to be.
That's my guess as well. I'm sure the equipment manager and ball boys are being interviewed by the league office. I'm also sure they wouldn't let air out of the footballs without someone (a coach or a player) asking them to. Unless these guys fall on their swords, they can implicate who put them up to it.