I have seen lots while diving, and I have kept them for several years. I know that books and article say they eat the tube feet of echinoderms, but I have never seen them with anything. The usual place I see them is when looking under rocks, they are almost always in prs, and I have seen urchins and stars under the rocks, but not near the shrimp. Mine eat anything meaty that I put in the tank, mostly frozen chunks of mysis or other shrimp, but it has to be small. They are very agressive to each other, unless paired up, I've never seen more than one pr under a rock, even large rocks.
As far as eating a star, I would believe an unhealthy star, and sand sifters are very hard to keep well fed, usually starving after extended periods so it may not be apperent to the owners that the star is unhealthy because of starvation, could be attacked by a pr of bumble bee shrimp, but I am not sure they would activly hunt a healthy star, at least not to the point of killing it