You are safe. I had a BT pair that never nipped or ate any coral or inverts.
One thing to keep in mind is that triggers are inquisitive, and may pick up and move around anything that isn't glued down. Make sure you glue down your frags.
Also: from time to time they may run into a SPS that is sticking out in the water column, and break it accidentally (all large fish may accidentally do this).
As far as CUC are concerned, my male BT used to search around the tank, and collect all of the hermits, and put them in a pile in the middle of the tank and watch them all disburse from the pile about twice a day for fun, but never ate or harmed any of them.
I have everything from open brains to digis, to polyps, duncans, anenomes, clams, hammers, frogspawns, etc... The trigger has never nipped at anything. At feeding time, when food lands on the coral, the trigger may swim up to the coral, and blow the food off and eat it as it falls off of the coral, but it never has mouth to coral contact...