Primary cause, probable cause, etc. etc. confuses many readers. However it does not confuse safety professionals (who read right by those words). The meat in a report is the linkage of the contributing facts with recommendations for prevention.
In my initial read of the posts above I sensed that the words "primary cause" was simply assigned to the last link in the chain of swiss cheese.
In other examples of the use of the words, it might refer to the most effective link in the chain to assign preventive action that addresses other combinations as well.