No fire?? Mmmmmm!
I appreicate that it's been said further back that fuel quantity wasn't a problem, and what are the odds that both engines would quit as a consequence of fuel exhaustion at exactly the same moment? Not very likely I wouldn't think, but perhaps one had quit a little earlier and they were on one, started to sink, firewalled the other, but it didn't have enough fuel to deliver the goods.
Speculation I know, but jet engines don't just fail without good cause. Eye/ear witness accounts can't be relied upon as indicated back a way; some heard it fly overhead very quiet and others heard the engines roaring.
I haven't flown a 777, but I'm sure safeguards are built in to prevent the autothrottle shutting down the engines, and you certainly can't do it manually with just throttles in any jet I've flown.
I hope my speculation is wrong.