Not only do they not move around corals, I have a nem (I think Heteractis aurora) that seemed to specifically want to sit on some this past week. It's a small nem in a small tank that had a few softie frags in it temporarily while I figured out where to put them. Bit of Anthelia, some little piece of toadstool, a bit of mushroom, and some sort of tree coral. The nem eventually outgrew a small rocky hole it was living in and then literally chased the frags around the tank no matter where I put them. This went on for a few days and it stopped and anchored down within minutes of me removing the last frag. I have no idea whether it was just desperate to sit where something else was sitting or if it wanted to nuke competitors, but it probably would have killed the frags if I left them be, since it would have smothered if not melted them. I don't know if that some unique strangeness to the species of nem, but you will definitely minimize losses if you let the nem have free range of the tank for a while. It's not just a risk to corals either - somewhere I recall reading about a BTA that got melted while trying to wade through some mushrooms.