If you're Republican-oriented, tired of having every scandal called back to Watergate, you can always use the alternate name: "BallGhazi"
How do you measure your balls?
If they stick a pin into the football to measure the pressure, it'll let out a little air each time.
If they measure at a lower temperature than when the ball was inflated, they'll get a lower pressure.
How do you blow up your balls?
Compressing air raises the temperature, so putting recently-compressed air, such as running a pump output directly into the football, will inflate with hot air. The pressure will decrease as the gas cools.
If you bubble the compressed air through a water tank before running it into the football, you can put water vapor into the football, and if the vapor condenses inside the ball as the gas cools, the pressure will further decrease because water vapor of much less dense than liquid water.
If you inflate from an storage tank at hight pressure and ambient temperature, you can get the opposite effect, because expanding the gas inside the football will cool the gas, making the pressure increase as the gas warms back to ambient.
If you inflate with hydrogen, you make them just a smidge lighter, but also use a gas that'll diffuse through the rubber and leather a little faster.
How do you treat your balls?
If you rub your balls, as for roughing up the surface, the fricton will warm the balls, temporarily raising the pressure at the time of inflation and initial pressure checks.
If you ream out the inflation hole, you can make it gape open a little, leaking air at a slow rate.
If you keep your balls warm before each pressure check, you can more easily pass the test, then let them cool down for the play.
So, if you fill your balls all hot and sweaty, you can pass the tests and have a nice soft balls to play with later. If the NFL doesn't update their standards, soon all the teams will figure this out. To avoid this, they should be inflating their balls from a big tank at ambient temperature and relatively low pressure.
If the NFL specifies the gas mix, a minimum tank size and maximum tank pressure there won't be such ability to cheat.