Depends on what your definition of reef safe means. When I see this question, I say, will it eat corals or not? If that's all you care about (which I do) then I'd say yes, they are reef safe in my experience. I actually just took my pink tail out of my reef yesterday. Over time he got just to large and very aggressive. I tried introducing another trigger to my reef and he tried to kill him.
Crosshatch, Niger, Blue Jaw, Pink tail, durgeon, sargassum, are all triggers I've done in the past that were reef safe to me. Once again, this is strictly based on will it eat corals or not. I don't care about shrimp and snails, etc...