Each puffet is different. I know for a fact that puffers can eat any corals (i only follow puffer threads). They are just less likely to eat soft corals. I know some toby puffer eating all LPS
and others who dont touch them. Please reframe from keeping your puffer "well fed" in attempt to decrease the chances of nibbling corals and other livestock. You end up overfeeding your puffer which lead to premature death. Feed once daily until tummy is slightly rounded. Its very difficult to starve a puffer.
A puffer may challange an invert with much greater size.