Here is one website that seems to lay it out pretty clearly.
Without more context, I would guess that the author chose past perfect in the example you give because he/she is referring to the distant past. In the event of a terrible accident, the newspapers would write, "None of the passengers were badly injured in
the accident." "
An accident" covers an unspecified period of time in the past when any of the passengers might have been injured, separately or together, in any number of accidents.
Here is a somewhat silly use of your phrase:
The Risk Takers' Club booked a test run on the
Why Not, the experimental ocean-going vessel powered only by hydrogen. Although they had participated in such dangerous ventures many times before,
none of the passengers had been badly injured in an accident. This time, however, their luck ran out.
[not a teacher]