Lots of Occam's Razor talk. Occam's Razor, to my mind, slices off the following slab of logic:
1. Brady prefers low pressure. (known)
2. The Pats' ballboys are very aware of this. (extremely likely)
3. Without Brady having to say "Hey, Stevie from Brockton, please illegally let air out of the ball after the refs check it after every game, especially in cold weather," the ballboys know that this is what Brady likes, and they do it, and they don't use any kind of gauge, they just kind of hiss out some air randomly until it feels a tiny bit softer. (conjecture)
4. The Colts, and maybe other teams, have noticed this about the Pats' balls. (known)
5. They tipped the refs off (known) and also made damn sure their footballs were 100% properly inflated. (conjecture)
6. Before the game, the refs, not being dummies, checked the balls with the official equipment they use to check balls. (likely)
7. The balls checked out. (known)
8. Stevie from Brockton did what he usually does to make Brady happy, which is let a little air out. (conjecture)
9. The refs, having been tipped off, checked the balls again at halftime and found them to be low. (known)
10. The fucking world went crazy. (known)
Brady can say he didn't tamper with the balls, or even order anyone to. Belichick can say that he had no idea about any of this, because he didn't.
Isn't this scenario -- parts of which have obviously been suggested by other people -- more likely than either referee incompetence in the face of a direct complaint from a team (and probably discussion with the league about what to do), or an extreme variance of the Ideal Gas Law, which very unluckily happened to cause the football pressure to drop lower than one might expect, which very unluckily happens to correlate to both (a) the way Brady likes his footballs and (b) the complaint registered by the team they were playing that day?
This whole thing is dumb, and the procedure clearly intends to allow guys to alter the gameballs the way they like them, within reason, and the tornado of nonsense swirling around this is humiliating for everyone. But given everything, if no one on the Pats' payroll altered the game balls in any way, shape, or form, then boy oh boy did they get unlucky.