This allegation would never happen again if the NFL provided the balls.
Now there was an example of illegal manipulation of ball pressure outside the “legal” range: During a Jets pre-game, the game official inflated many of the Patriots balls to around 16 PSI, which is high enough to start spreading the seams, and apparently what got Brady and the training staff to find out what the actual pressure rules were and start informing the Referees - so they’d get it right.
The NFL would be the one solely responsible for ensuring every ball was exactly the same.
Once all the balls were properly inflated based on their own rigorous guidelines you could put them in a bag and someone could randomly pull out a ball.
The balls should, if the NFL followed their own rules, all be exactly the same. Neither team could manipulate the air pressure.
If the problem is teams allegedly manipulating pressure to their advantage that problem would be eliminated once and for all.