As the organization grows, does it become harder to communicate the strategy to everyone in the company? Does everyone still need to know the whole strategy, or can they get by with just knowing what their part of the company needs to achieve?

There's a common safety poster you find hanging in a lot of workplaces that says, "Safety is everyone's responsibility." Is the implementation of the strategy similarly everyone's responsibility? And if so, do you exempt people from that responsibility if you don't communicate the strategy to them?