Both teams don’t use the same ball.
I'm fairly sure that it was said during the original controversy that each team brings a certain number of game balls to a game and they have to be inspected by officials before the game.
They use their own approved footballs during a game. Any tampering with pressure would have to have taken place after the balls were inspected by officials.
Seriously? Why the eff not? Every other sport they do save bowling and croquet. Tennis, basketball, soccer, kickball, baseball, for cripes sake.