All of this talk about BA/Boeing/GE/insurers making decisions to repair or not to repair based on wanting to avoid a bad record or reputation are bunk. First, all of these entities are sophisticated profit-maximizing entities. They will make their decisions based pretty much completely on the basic economics of whether repairs cost more or less than the replacement cost of the frame. Note that based on recent statements by Delta Airlines, used B777's are going quite cheaply, so the cost of these repairs cannot be more.
Further, while if you bang up your automobile, you may decide to repair it privately so as not to alert your insurer and maybe cause your rates to rise, this situation is completely different. The incident has occurred and has been widely publicized. Every airline or insurer who has an interest in these matters already knows that this BA B777 had an engine failure and fire. If it is going to affect BA's insurance rates or BA's or Boeing's or GE's reputation, it already has. No repair/replace decision made now will affect things.