I think the best explanation for this is the pressure with which the ball is gripped. Players are squeezing and hanging on to it for dear life. Refs are just resting the ball in their palms with probably minimal pressure with their fingers.
It’s worth considering that football players are enormously strong and players that handle the ball have hand strength far greater than an average male. Someone with average hand strength probably couldn’t feel any difference between a ball inflated to 10.5 PSI and one inflated to 13.5 PSI because in either case it would feel hard as a rock.
I had to go back through your post on this subject.
Are you sure you know who the pats played last sunday ?
:)