Anyone remember Ben Coates bouncing his g/f off a car? Irving Fryar being filleted by his wife? Zeke Mowatt showing "Little Zeke" to Lisa Olsen? The mosh pit? Some guys named Bryan Cox, Corey Dillon, and Randy Moss? Rodney HGHarrison, the supposed "dirtiest player in the NFL"?
The problem with public perception is twofold.
In general, people think their athletes are heroes. In reality, they're just men, with all the problems that most men have... to wit, they're probably assholes. Every team has them. There are guys with drug issues, gun issues, speeding in their car issues, rage issues, performance and effort issues, whatever.
In specific, people think "the Patriot Way" means 53 altarboys. It doesn't, and it never did. It's about 53 guys playing unselfishly to form a T-E-A-M with the ultimate goal in mind being winning a Super Bowl.
The Randy Moss of youth was too immature, too concerned with himself. Age educated him to the point where he began to realize that the missing ring was more important. Same went for Corey Dillon. Same probably goes now for Chad.
Now, as for Haynesworth, it's going to be up to him. If he comes in here and makes it clear that he's only interested in winning, then he'll get along fine (at least for a while, hopefully through one season where the Patriots win a Super Bowl and Haynesworth sets himself up for a fat contract somewhere else). If he comes in here and makes it clear that it's all about "me, me, me", then he won't be here for long. Either way, it's not a distraction because the other 52 guys already get "the Patriot Way". Gronk and Welker and Brady and Mayo and whoever aren't suddenly going to say, "Hey, this guy's right! It's all about me too! Screw the team!" Not gonna happen, not with the environment created by Belichick. This is why only the Patriots can take risks on these kinds of guys and either a.) get something out of them or b.) have it be a "no harm no foul" and cut their losses.
Do I prefer they'd signed some stud without issues? Sure. But there's a reason you get guys cheap: it's because they're coming off injury, or old, or have some sort of attitude problem or legal problem or whatnot. We wouldn't have GOTTEN the Dillons and Harrisons and Mosses otherwise. And we wouldn't have gotten "$100M" Haynesworth for $5M and a 5th, or Chad for two paltry late-rounders. That's why it's a risk-reward scenario. You want studs without character issues, you draft 'em high or you find diamonds in the rough (Brady) and you pay them big bucks.
It is what it is.