Ok, so you weren't wrong to say 8 of the top 10 in PPG were top 15 in Punts inside the 20%. However, this theory doesn't really hold up in other years in the data set. Also, I've shown no strong correlation. There also isn't a strong correlation between YDS/G and Punts inside the 20 %.
Despite the fact that we haven't found any strong indicator that punting affects defense in a meaningful way this did prompt me to do one more data set, and that is Win % versus Punt IN 20 % and that has given the strongest correlation of all data.
This is surprising, because one would expect that if they did affect W% they'd also affect Defensive performance. That really doesn't seem to be the case.