Because there is no exact definition of "reef safe." It means different things to different people. I personally only take "reef safe" to mean safe with corals. As pretty much any fish we keep will eat inverts (does anyone's tang not eat mysis? ). Also because I strongly disagree with the brainwashing that everyone "must" have a clean-up-crew, but that's another topic.... It sounds like the book is just inferring that the Six Bar wouldn't eat ornamental inverts (cleaner shrimp, emerald crabs, etc).
If you are interested in finding experience with Six Bar's, I suggest you look for people's experience with Blueface Angels instead. SixBars are unfortunately just not really kept often in this hobby (a shame really, a gorgeous fish in person). Bluefaces are very closely related to Six Bar's, they once were even grouped together in a unique genus, Euxiphipops (along with the Majestic Angel), before ichthyologists moved then into the Pomacanthus genus.
My personal experience with my Blueface is that he left frogspawn alone (I was surprised and wouldn't put a guarantee on anyone else's), he nipped my mushrooms occasionally, and he devoured any zoas.
