I think a lot of the problem is different view concerning the role of the DM, whether the DM is the storyteller or the world builder and referee.
In the vision of the referee as storyteller, it is the DM's job to make sure everyone is entertained and having a good time. It is his/her job to make sure that everyone shares the spotlight equally. In this vision, asymmetrical stealth is a problem because it difficult for the DM to entertain each player equally and give each player equal face time. If you're group sees the DM as a storyteller, you might be better off using group stealth checks.
If you're group sees the DM as a world builder and referee first and foremost, group stealth checks upset the underlying principles of the world, namely that someone trained in stealth can move so quietly that he/she can somehow make up someone clanking down the corridor next to him. Player-driven sandbox games require the players to have a basis in the physics of the game world in order to make informed choices. The easiest way to ensure that is for the mundane (non-magical) elements of the game world behave as they would in ours. Therefore group stealth checks would be ill advised in this vision of the game.
Which vision your group uses may determine how best to make use of the guidelines presented in the PHB, MM, and DMG.