Except, the NFL weighs the balls. Although PSI is subject to temperature, weight is not.
Weighing the balls would prove nothing. The weight difference (assuming constant temperature measurements and that the underinflation is due to allowing gas to escape) would be on the order of 175 milligrams (about 0.006 oz.). I highly doubt that they are using a scale that can detect that weight difference in an object as heavy as a football.