Though I agree with the spirit of your post and think you made a number of good points, we were very good at running the ball last year. 6th in yards, 7th in yards per attempt, by any measure we were very good and that's a departure from previous years. Not dominant, but there wasn't a team as offensively balanced in football last year.
The other distinction that analysts aren't making is that while we were 26th in the NFL in terms of passing yards against, we had an excellent pass defense when we weren't fielding a secondary composed of Malcolm Jenkins, Chris McCalister, and Mike McKenzie. Even with those guys playing for significant stretches of the season, we still finished third in defensive passer rating and fared well in meaningful stats like completion percentage, YPA, and were outstanding at forcing turnovers. But if you only look at the yards number, which 99% of analysts do, you're going to come to a conclusion that simply wasn't true about the Saints pass defense. If one flaw of the media is failing to account for the fundamental change to a passing league, the other is failing to look at more meaningful numbers. Football has been among the slowest of sports to adopt advanced stats, and that's a shame.