I'm not 100% on this because I haven't specifically tested it but I believe you can get looting rights (when not partied because obv you get looting right in a party even if you do nothing) if you heal enough damage without actually needing to do much if any damage. I'm not sure what that amount is or if it varies but I have gotten looting rights at places like UWB by primarily healing people (not in my party). The char I use is a Tamer/weaver which can no longer use a pet and has never been able to WoD so outside of maybe 4-6 earth eles I don't do much damage but I always get looting rights as long as I'm not getting there near the end (ie the UWB has over 25% HP - or so).