[cornholio]

In an emergency, the safest way to burn fuel is to reach the closest airport and then circle it. Not head to a more distant airport which you might not reach because of the very emergency.

All hypotheses will invalidate the major premise: that the pilots chose that particular heading not randomly, but in a calculated attempt to reach the nearest airport because of an emergency. Basically, no matter where the plane would have turned, if you draw a long enough line you will find an airport. But that does not explain anything.

[ams6110]

In a dire emergency, you would just dump the fuel and not try to burn it off.

[deaks]

Except, the 777 does not have fuel dumping.

It was not required for certification because it meets the minimum required climb rate with an engine failure after takeoff at Max Gross Weight.

[gergles]

Yes it does:

http://cdn-www.airliners.net/aviation-photos/photos/7/4/7/23...

Look at the top center, at the "Fuel Jettison" switches. (This is a 777-200 non ER, but I doubt the ER model would remove this feature.)

[nickff]

Or even land heavy.