One of the definitions on safety culture is "the way one works even when nobody's watching". If an organization functions truly the way even when there is no monitoring, as it functions under observation, then its culture is said to be good.
If everybody works safely without monitoring / reminding / without the need for display of posters, slogans, etc then really safety culture has been imbibed in their blood!!!.
It means, there is no need for safety department and can be disbanded as every employee has taken that role on himself.
A leader should not get blinded by reports from few lieutenants / spies (the spoilers who increase the distance between the leader and subordinates) in the organization to know what is happening. Everybody should be able to communicate to him so that he gets a fair idea of what is happening and how things are moving in the organization. Once such reporting is established, it aids in safety culture also.