They have the power to hold an FAI into any death in the workplace, or where there is a belief of suspicion regarding the circumstances of death, including service deaths.
I don't beleive, based on the Crown Office interpretation of employment, that discrecionary power extends to service deaths where there is no suspicion, where as a 'normal' workplace death would invoke an FAI.
I'm interested to see if COPFS manage to cite the cases they mention, there is sometimes a tendency to rely on Stair et al without double checking.