In the CV and especially the CQ enviroment dealing with a lot of new students, the direction from the ship on where and when to go to the beach and in what configuration is quite common. For those who do not know, here's how it works.
Each squadron has a "rep" in the tower standing next to the Air Boss (in charge of the flight ops) who will get on the radio and talk to the pilots when something happens. Based on the info collected by the rep and/or boss, the air boss, rep and sometimes the CO of the ship will decide what to do with the plane. The decision is then passed to the pilot and 99% of the time that decision is what will happen. IE, you have a single engine and your signal is "divert to Mirimar." At that point there is little discussion. You divert to Mirimar unless you are certain you aren't going to make it. If the boss tells you to bring it back to the ship, you do that as well. The "I'm the pilot and doing what I want" idea goes away a little operating at the boat. You do have the absolute final decision, but if it goes against the ship's reccommendation, you better be 100% correct and let the ship know what and why you are doing what you are doing!
Now, there are plenty of questions of who said what here, but if the pilot was told to take it to Mirimar, that would be done with little question. Especially if he only had a single engine situation at that point. Don't know when he got a low fuel light, but that should have turned it into land ASAP and then it is totally up to the pilot in command.
Sorry for the long post and obvious info for those who've been to the boat!