you invoke Occam razor, but i don't think it helps your case: by far the easiest explanation is that they cheated and then they lied about it, not that by some curious coincidence only some specific balls 'lost' some air, but none of the presumed beneficiaries knew anything about it, or that the refs mismeasured only some of the balls. or some other conspiracy theory.
What is this 'simple' explanation of yours?
Here is what I meant by Occam's razor: I don't trust the league or the referees. To me, the simplest explanation is that they weren't checked before the game with a gauge. And here's why: (emphasis mine)
Could the NFL be covering for its officials with Deflategate?
Eric Kester, who worked as a ball boy for the Chicago Bears in 2003, said part of his job was to work with the quarterback before the game to prepare the balls.
“We would then work with the quarterbacks to customize the balls to their liking,” Kester told Monica Alba of NBC News. “This involved scrubbing them with stiff horsehair brushes to rub off the leather’s slippery silicone sheen, and occasionally inflating or deflating the balls a very small amount, which I believe is legal to a degree. Quarterbacks are very particular about the way a ball feels in their hand, and we worked meticulously to match their particular preferences.”
We knew all that, but the next thing Kester said strikes me as incredibly interesting. Based on his experiences, the referees did not always stick a pressure gauge into every ball.
“I recall them having a pressure gauge in the locker room, but most often they just squeezed the balls, turned them over in their hands a few times each, and inspected the laces,” he explained. “I don’t recall them ever rejecting one of our balls.
“My thought process was, ‘Let’s get the balls exactly the way our quarterback wants them, and if the refs reject one or two before the game, no big deal. But there’s no harm giving them our ideal balls and hoping they make it through inspection.'”
Is it really all that unreasonable to wonder if the officials who checked the balls before the AFC Championship Game went with the “squeeze test” instead of measuring the actual air pressure? And if that did happen, would they admit to the NFL that they did not do their jobs the way they were supposed to?
I think this is dumb regardless (and I think most QBs in the league would agree), but if it is something people feel needs to be crusaded against, they need to have some clear evidence of tampering.
Again, the NFL has been extremely vague:

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