An NFL ball is supposed to be inflated 12.5 - 13.5 PSI. Each team is responsible for providing game balls. Each team personnel can scuff the scrimmage balls. Balls for Kicking (”K Balls”) cannot be scuffed.
An under-inflated ball would certainly be easier for a RB to hang on to. To a point, an under-inflated ball would be easier for the QB to grip when wet, but if too under-inflated wouldn’t throw as well.
Remember folks the offensive co-ordinator & QB coach for the Patriots is none other than Josh McDaniels. He was caught up in a cheating scandal while head coach for the Broncos. It was during the annual London game and it had to do with one of his assistants taping the opposing teams practice session. The Broncos later that same season fired McDaniels and the taping scandal was cited as one of the reasons.