Engine out
Im only a lowly fATPL and as far as I can see the aircraft commander made a decision, the safety was judged to have not been compromised and would assume that this was discussed with the F/O to the continuation of the flight.
One can only assume that all the relevant calculations were made, including divert inline with over the water flights and that minimums were carried to the destination. Also the MEL would have been consulted and probably there ops
Im sure the 747 could have diverted on 2 engines, I reguarly fly to US on twin jet ops (as a passenger) but the loss of 1 engine is a concern but not a panic as I am sure the eventuality was covered in there planning.
If that was done, what is the problem!!
Excuse me if it seems ignorant, I have read the posts start to end !!