In general, I'd say it's part of the exec's job to ensure that the right sort of culture is set where individuals feel empowered to surface relevant information. This includes trying to make sure that people feel safe enough to surface issues, getting rid of people that aren't good about responding to feedback, etc.
As a corollary of this, you can tell when an exec is bad since not only do people snark, but the same topic of snark lasts for years and years.
There's also a part of their job to have the right organization structures in place such that if a piece of information should really get resolved at a lower level, it does. If a lot of information is having to be resolved by an exec, it probably means an organizational refactoring should probably be happening in the first place.