Making it easier to throw and catch is a distinct advantage in a league that has done everything it can to make the passing game easier. Especially, when the other team is actually following the rules and do not get that advantage. Another, especially, is that you KNOW, they have been practicing with deflated balls, too. It's not like they just decided to do that for this game to see if it would work.
In any event, anyone who can't see this as a clear advantage and had nothing to do with the score, is blind. We can also go with the old saying "if it didn't give an advantage, why did they do it with such a large portion of the balls they used, and risk all that could be lost by doing it?"