For instance, if she died from food poisoning on board and just happened to stumble overboard just as the ship was sinking, or if the Navy accidentally bombed the ship as part of aerial bombing practice,...
Here's a great example as far as Captain responsibilities go. If she died from food poisoning, did the Captain immediately contact the CG or the authorities, quarantine the food, treat other sick crew members and make for shore?
If she fell overboard when the ship is sinking, did he make sure or delegate his subordinates to ensure that everyone has their PFD on and are aware that they are about to abandon ship.
If the Navy destroy the boat during bombing run practice, did the Captain get all the pertinent information he needs in regards to his sailing route before he proceeds out to sea? As pilots, we get what is call NOTAMS (Notice to Airmans) so that we don't stumble into the Military Operating Areas or Restricted areas. Airplanes have been shot down for such excursions.
As I said earlier, no matter what, all the final decisions and responsibilities rest on the Captain and the Captain alone.