The Fire Swith does close the Spar Valve!
Mono, Silent Badger, ...
If all things are still in one piece, the fire handle does close the spar valve on the B777 (see, e. g. the diagram in Section 6.7 of the Flight Manual. I only have seen it for the GE90 variant, but someone posted the equivalent for the Trent in a previous thread).
The report is quite clear on that, just read it carefully. In B777 aicraft not modified according to SB 777-28-0025 there are two separate wiring paths to the spar valve, one from the cutoff lever, and another one from the fire handle. The fire handle, in addition, also isolates the wire path from the cutoff lever, so that the cutoff lever will no longer be able to shut the valve.
Hence the original Boeing checklist for evac and engine fire specified to close the cutoff lever first, and only then activate the fire handle. The BA checklist split the two tasks between the Cpt and F/O, thus creating, as we would say in computer science, a "race condition".
In the case of BA038 the path from the fire handle to the spar valve was damaged, and although the path from the cutoff lever to the valve was ok, it was isolated by the fire handle, which on this occasion was activated before the cutoff lever.
This left the spar valve open, which, in combination with other damage, caused fuel to leak from the aircraft, which, luckily, in this case, did not cause a fire.
With the desirable sequencing (cutoff first, then fire handle) the spar valve would have closed. Althought not causal to this accident, it would have reduced the risk of fire, and therefore merits the safety recommendation.
Bernd