I agree that those text messages look like something that is not above board. More than likely, the Pats had tried to develop some system for "correcting" wrongly inflated balls. Remember those text messages refer to Brady being incensed about a 16 PSI beachball? The refs found some of the Pats balls lower than 12.5 and over-corrected.
And let's think about this logically. If the goal is to get the balls as low as possible, then this situation of ref correction is extraordinarily likely to happen. Rodgers described the same situation in reverse, that he would ask the equipment guys to get as close to 13.5 without going over. Because if you get out of spec, you have lost control over the eventual pressure of the ball as the refs will correct it.
This is something that competent administrators would work through. If there is something amiss, what is the corrective measure? I doubt the answer to this question in the manual is to make it 2.5 PSI above the legal limit. BTW, this is a sign of exactly how unimportant the NFL saw this issue until the Ravens and Colts came bellyaching to a former Jets official in the League office. This is why a patient and non-maximalist approach should always be preferred. Prior to the game the only people that cared about this were QBs and 3 officials that were pissed at the Patriots handing them their hat for over a decade now. Goodell, reacting like bad news is a mallet to his patellar tendon, was now chasing leaked false info. And that info was about an issue that did not affect the outcome of the game. It just pissed off three opponents.
I maintain the next likeliest scenario is that this was ALL about pre-inspection ball prep. You have to be careful to go low as you can without raising a red flag with the refs. That limits what you can do pre-game.
Third most likely, as no other ref has reported the game balls went missing before a game, is that the events of this playoff game were an anomaly. So if the Patriots text messages (from earlier in the season) are an indication of an illegal scheme, it most likely happened on the sideline, not during transport while the refs were there.