As one poster put it with sat phones and data link the crew have access to a lot of information on which to base a decision. I doubt the crew would have continued if they thought that they had a crippled aircraft.
I do have to question though some of the assertions that just because its a STATUS msge then all is well. The 777 QRH is a very thin document compared to a lot of other Boeing QRHs. Thats due to most abnormals consisting of STATUS msges that don'e require any crew action. My understanding of the reason for this is that Boeing tried to make the 777 that automated even with non-normals that no crew action was required. As an example of this the 777 did not have an unreliable airspeed checklist because the FT-ADIRU was considered so good that in the event of a single failure of an accelerometer or gyro then the "box" would take care of the problem without the crew having to do any switching. After the MAS 777 incident in 2005, Boeing have now put an Unreliable Airspeed checklist into the 777 QRH.