Fumbling players being treated harshly by their coaches is true of every team as far as I know. That said, I still think it's more likely that the Patriots have some unique practice/drilling regimen that results in less fumbles than they are regularly using deflated balls to their advantage. This is interesting in and of itself, so no matter what, I think this is an interesting analysis. But it's hard for me to believe that they were regularly using under-inflated balls for FOUR YEARS before being detected (or perhaps I should say reported).
Of course, giving the context of its publication, we know what it's trying to imply.