You can't isolate one factor as the cause for fumbling or not fumbling. I don't believe that deflating the ball has any impact - zero, none, 0.0. If the Patriots really do fumble less than other teams, I think it would more likely relate to personnel than the football. I'm pretty sure BenJarvis Green-Ellis had but one actual football skill, and that was not fumbling the football. Meanwhile, poor Stevan Ridley could not stay on the field because he couldn't hold onto the ball. Presumably they were using the same football, so that would lead me to believe that any lack of fumbling has nothing to do with the ball and everything to do with the guys carrying it. I didn't read to find out where they got the 16000:1 ratio, but I can tell you it is absurd and not believable on its face. I find the desperation of people to try to make this a serious competitive issue to be hilarious. I mean, the Patriots were caught breaking a rule. You have them dead to rights on it. They played with underinflated footballs. So give them their 25k fine and strongly worded letter and let's move on? Why embarrass yourselves pretending like the amount of air in the ball has any effect on the game?
Having said that, though, I do think this has probably been going on for a while. They probably prep the balls the same way every week and if it gets by the refs because they do a "squeeze check" then that is what they play with. But to try to make it into a bigger conspiracy or something that actually effects the game on the field is insane.