I like to consider all aspects of a football team so I enjoy a power running game paired with a strong defense and efficient special teams as much as a high powered vertical attack that needs to light up the score board bc their defense will likely be giving up points as well.
In a strict evaluation of the Saints offense (also true for the Pats, Colts, Packers, Lions, etc) I think what's important is looking at where the best players on your team are and how to allow them to have the greatest impact on the game. Brees is the best player on the team so why not design plays that have slightly more risk than a run (in terms of success, turnover potential, expected yards, etc) if it naturally incorporates parts that also allows your best player to shine? For example, a play may result in a short dump off to Sproles 90% of the time but the first couple of reads are for a skinny post and a go route... not to mention the defense reacts different to a Brees drop back than a straight hand off.
Now if your best player is your RB or the collective stars are on your defense, this approach doesn't make as much sense (hearing me Cam Cameron?). I don't have a problem with the number of passes Brees throws because it's an effective and successful approach for the Saints. I do have a problem with ignoring the fact that teams run different strategies (and even similar strategies to different extents) and zeroing specifically in on stats to decide what players are better. There's no reason to criticize Brees or his very legitimate record. Hell, the fact that he's allowed to throw the ball that many times speaks of his greatness even if that's the only thing the record represents. But we shouldn't ignore these details when comparing players.