I am also uncomfortable with the "everyone is responsible" mantra. resposnsibility balances with authority; you can't be considered responsible for something which you have not the authority to address. Safety (at least in the short term) is expensive - though the comment "if you think safety is expensive, try having an accident" is very true. So the people "responsible" for safety must also have the authority to make the necessary allocation and diversion of resources.
Everyone can - and should - contribute to safety.
But responsibility lies at the top - and even if they delegate the conduct to middle managers and safety specialist, they are STILL, IMHO, "responsible".
My fear with the "everyone is responsible" idea is that it dilutes the real responsibility. By analogy, the Chief Constable is responsible for the conduct of his force; rolling out a "we are all responsible for keeping the streets safe" campaign dilutes his responsibility not one iota.