So what we have is an agency that is entitled 'Occupational', but it is also responsible for public safety?
Actually, in my opinion, what very likely happened is that the various public safety divisions that used to be stand-alone agencies were at some point grouped under DOSH.
The inspectors that caused all the trouble at DL have no idea how to inspect any of the specialty items, such as boilers of elevators. They are more the fundraising arm of DOSH than anything else. They would look right at a steam boiler that had it's high-pressure relief valve plugged, and wouldn't recognize the hazard. The boiler inspector on the other hand........
These inspectors don't cite things that are a hazard to the public, that's the job of a different division of DOSH. They only inspect things that effect employees.
So yes, DOSH does indeed have some responsibility for public safety, but depending on the particular division you're dealing with, they might not care about the public.