professional crews do not shut down a perfectly good engine unless it can absolutely be shown there is a major need to do so
No they don't. But a professional crew would be guided by the checklist!
From the ATSB report .....
After completing the appropriate ‘non-normal’ checklist items, the crew shut down the number-3 engine
I guessing one of the checklists that would have been of some interest would be the Fuel Leak checklist, which a previous poster has already mentioned!