I graduated from a Maritime Academy in 2007 with a USCG 3rd Mates unlimited tonnage license and spent May 2007-February 2017 (just took a shore-side job a few months ago now) as a deck officer on civilian run ships...2007-2011 on civilian manned USN ships (cargo and special mission ships for the Navy are run by civilian mariners, not active duty military) and then 2011-2017 on drillships.
I spent a total of about 3-months on actual USN ships (as a cadet only, 2 destroyers and an amphib) as well as countless hours sailing alongside them (as 3rd and 2nd Mate) during UNREPs and just general navigating in the vicinity of them, here is what I know.
USN ships are manned by an abundance of bodies, I dont recall there ever being less than 6 or so and often times 10+. In my time as a Mate we rarely had more than 3, most often 2 and it was not at all uncommon for me to run the bridge solo. While it might seem having 6-10+ on a bridge makes it safer I would disagree. One trained mariner running the bridge solo will focus on the task at hand while multiple guys on a dark bridge underway at night can very easily fall into complacency, thinking "someone else" is looking out.
The USNS ships I sailed on all had autopilot of course, however none had any sort of auto-nav features...meaning I would enter in the compass course I wanted the iron mike to steer and the vessel would maintain that heading, no further input went into it. It did not account for set/drift, it did not adjust speed up or down, it simply held a compass course. The mariner would need to adjust as required to stay on track, follow the plotted track line, or adjust for traffic. Now I cant say for certain, but I am quite sure DDG's in particular are setup with the same systems, a "dumb" autopilot if you will.
The much more advanced drillships I spent my time on did infact have systems where I could plot a track and tell the ship to follow that specific track. It would adjust heading (to adjust for set/drift) as needed to keep the vessel within X-meters of the trackline, and would actually change heading as needed on waypoints to follow the track. In my 6+ years on those ships we never once used that system for anything other than just testing or "playing around" with it during trials etc. The very idea of putting control of the vessels piloting in the hands of a computer system alone would be crazy to any trained mariner.
Now at this time I need to mention...the sea is FULL of ships and mariners from all over the world. US and European mariners in particular are very well trained and follow the "rules of the road" quite well. A lot of asian, middle eastern, and other places Mariners....not so much. For us a 1 nautical mile CPA (closest point of approach) is acceptable. To a Phillipino mariner? Not hitting another ship is acceptable. So there are different standards.
If I had to speculate here is what I think may have happened. The container ship was infact in an auto-track mode, with a mariner "on watch" that was either sleeping or a few decks down making a sandwich or who knows... The USN ship was underway and saw the cargo ship on its current course/speed and did infact have an acceptable CPA (closest point of approach). The container ship came to a waypoint in its track and on its own made a course change that put itself on a collision course with the Destroyer. Now at this point the only real reason I can see why the Destroyer would not have made the necessary change to avoid collision is that they did not realize the container ship changed course and was now on a collision course. Whether they werent paying attention or what I cant tell you, but if they were maintaining an acceptable CPA the entire time prior to then the cargo ships course change wouldnt have put it into a collision immediately, they would have had time to maneuver.
Maybe the Destroyer tried contacting them via VHF either prior to or during being on a collision course...or maybe they didnt...it doesnt much matter because its very common to try hailing a foreign flag cargo vessel on VHF to discuss passing arrangements and get no response, that isnt something that necessarily raises red flags. USN ships typically contact other vessels via VHF unnecessarily anyway, in my experience it often creates a more hazardous situation when you try discussing arrangements with non-english speaking mariners and is usually better to SHOW them what you want to do with your ship, meaning make a large course change one way or another so its obvious what you're doing, versus trying to talk it out over the radio.
Its hard to speculate just based on the little info Ive read, but ultimately both vessels are at fault when a collision occurs.