Well, we don't have an exact quote from AR, it was told secondhand, but your point is still correct.
We do have a quote from Aaron Rodgers:
"There is, if you don't have strong grip pressure or smaller hands, an advantage to having a flat football, though, because that is easier to throw. So I think that is something they need to look at. There should be a minimum on the air pressure but not a maximum. Every game they're taking air out of the footballs I'm throwing, and I think that's a disadvantage for the way that I like them prepped."
Why would the officials "take air out of the balls" unless they were overinflated? And why take air out "every game" unless you deliberately supply overinflated balls "every game"?