I've kept shrimp with Fungia in lots of tanks. The shrimp will scavenge on dead/dying tissue, but I seriously doubt they are the cause of the corals' death.
Heliofungia - long-tentacled plates, are more difficult to keep, and if they get damaged, they're done. Fungia or Cyclocyris (short tentacled plates) are much more durable, and I've seen Fungia survive awful conditions and one even survived a Rio pump meltdown. It closed up tight for about 2 weeks and looked totally dead, but knowing that the skeletons sometimes produce offspring, I left it there, and eventually it opened back up. It had been in that tank 9 years as of the last time I saw it - it could still be there now.
When sand sifting gobies drop sand or shells, that can irritate and injure the coral - it certainly would injure a Heliofungia. Fungia are usually a bit more resilient and they can sort of inflate and deflate to sweep the sand off, but if it continues constantly, it can and will stress the coral right to death.
Jenn