I'm not saying the Saints are innocent, but there are always teams with more or less of a rep for playing dirty, for whatever reason, and most probably do deserve it. With steroids, I know that all teams have that problem. But Goodell didn't make it a pet project to clamp down on steroid use (for good reason--it would change the nature of the game fundamentally if steroid users were taken away), so players get slaps on the wrist if anything at all. Teams, collectively, may be more or less innocent, but many of these players are amoral thugs who enjoy hurting other guys. Look at James Harrison and his attitude. He's better and more outspoken than most, so he gets more attention, but he's not special in his attitude.
The role that Williams played is really unfortunate, and ultimately, stupid and arrogant on his part, and he deserves whatever he gets. I think Payton and Loomis were also too arrogant to do their due diligence to reign in Williams, and for that, they deserve their punishment as well. But as for hits knocking guys out of games, I haven't seen more of that with the Saints than with anyone else. And in fact, I've seen teams like the Ravens and Steelers laying guys out at what must be a much higher level, because of their style of defense. Does that make them dirty? Not sure what other kinds of dirty plays you've seen from the Saints over the years, but they've caused fewer headlines than other teams and players for that kind of thing, and that's gotta say something.