The phrase قناعتهم بمرورية الحادث means that the family have accepted the cause of death being a traffic accident (also called road accident, road traffic accident, vehicular accident, motor vehicle collision, etc.). The key point is that the family has accepted the cause of death as reported to them by the authorities. In this case, it happened to be a traffic accident. In other cases, it might have been something else. This key point is implied but not stated in the Arabic phrasing. In English, you can choose to keep it implicit or make it explicit, hence the two options above.