You forgot another coach who didn't police his team: Joe Gibbs.
He actually took veterans aside and told them--and I quote--"This is your team". He told them he wasn't in the locker room, he wasn't with the players off the field...and that he needed the veterans to set the tone and help the players stay accountable to each other instead of just to the coaches. He told the vets that he couldn't/shouldn't do it, and that he needed the veteran players to remind the rest of the players to take ownership of the team, of each other and of everything that occurs in practice and on the field. In other words, to actually be leaders and provide the leadership every team needs.
That's not exactly a unique thing to do with the vets. Lots of coaches have done so and still do. And it's not as if this made the players no longer afraid of Gibbs if they strayed from the "foundation" Hatcher mentions...just the opposite.
Belichick's "complete control" works...if you're made up of the same stuff that Belichick is. Gibbs "players take ownership of the team" way works...if you have the right veteran players to talk to. I think Ryan Clark, Barry Cofield, Santana Moss, D'Angelo Hall (yes, Hall lol), Brian Orakpo, Trent Williams and Hatcher can be the right veteran types.
Maybe by comparison, the Cowboys are more of an employer/employee type of deal...Garrett and Jerruh micro-managing everything, veteran players' years of experience being overlooked too often...and players going to coaches to complain (or even worse, the GM) instead of handling things within the locker room among themselves ("that’s the way it’s supposed to go, through the players and not the coaches"). When you have to answer to the entire locker room and not just the coach, it makes a difference. And let's face it, it's not as if former Cowboys players haven't been talking for years about the lack of leadership on the team.
And seriously...who here really thinks Hatcher meant the players will have the ability to override the coaches on anything? lol...That's a laughable thought. So maybe he's just reflecting on how he feels he's part of a team now instead of being an employee of the Cowboys.