A lot of very good advice and corrections given by a lot of very knowledgable fellas.
Interesting how this crew is to be taken to task on the hear say of a third observer at the limit of VHF coverage. There a lot of factors that non of us will know without waiting for an investigaton, and perhaps even letting those in the hot seat give a discription of what really happened.
Without knowing how far they were from the nearest airfield (best TAS for a 777-300 happens to be at F330!!!...hence quicker to airport, than say at F180 so quicker to land perhaps?) what the wx was like etc etc...I think its pretty petty to say they did wrong.
For information this third world airline has some very modern stuff. These airplanes download some very nice info to maintance on the ground at operations, and by contacting them (if you have time) you can find out a lot more information to help you make a decision.
But please do not let a lack of information of what really happened, stop you from jumping in with the what you would have done better stories.
I guess it would be unprofessional to wait to hear the facts first.