I guess, as always, these things vary away from base. My take is the vast majority of the (BA) outstation staff do go out of their way to help, though for various reasons this can be limited by lack of practice (good!), lack of efficiency or lack of comms back to London to okay X or Y.

Can certainly recognise the Lusaka example above from personal experience (mostly good recovery on BA's part). As a WT passenger in those days I even managed to get checked in to the hotel before the 'official' transports got in.
The problem was, and still would be at LUN, there ain't much anyone locally at BA can do for you until a decision is taken on how long the plane will be 'out' and thereafter wait for London to give any authority for re-routes. Those with status did not fair that much better than my family did (IIRC) in terms of jumping ship sooner, but probably rested more happily in the knowledge that they would be the first sorted once things got moving again.