I think it's possible to overthink this to the point of becoming frozen or explain away a reason to come up short of what would be effective. To understand it in full context, we can apply Plan-Do-Check-Act in safety systems also.
Planning the system to avoid nonconformances that result in accidents, including how to capture and record data that will help understand results.
Doing the things we planned in the way they were planned, including data capture. This also includes accident investigations data, which I am placing in the "Do" category because accidents typically aren't part of the planned system. They are consequences of things gone amiss. Since I wouldn't want to wait for management review to correct a systemic problem if it presents imminent risk, corrections can happen in this part. In other words, "Doing" includes the "Planned" nonconformance process, one which ideally exists within management circles and doesn't rely on an internal auditor to raise an issue for action.
Examining the data to understand what needs to be improved upon systemically. This is done with periodic routine checks. Management can use this chance to plan capital or systemic improvements that, through careful review, they determine will be effective in preventing nonconformances that result in accidents. This might even include adding a specialist to provide expertise and manage what they decide they can't, or choose not to do on their own.
Acting on what was learned means applying the learning systemically, to raise the bar a little and trend down the incidents and accidents that can be quite expensive to deal with. An example is in fall protection. If an accident happened on the loading docks, a robust P-D-C-A action would include improving fall protection systems on the docks, but also elsewhere in the organization; it might include training, buying equipment like harnesses and installing railings. It might even involve rearranging the work flow to avoid activities that are particularly risky - finding a new, smarter way to get the work done.
The standard does tell us to do these things, just not in the words I used. Doing these things would also help protect from the kinds of mega-$million fines that, for example British Petroleum was assigned following their Texas plant blast some years ago. In their case it wasn't just the accident that did it; their fines resulted in investigation showing their Plan-Do-Check-Act had been hollowed out to the point of being just a slogan.