I think that it is possible that the family has been given information by LE that indicates that Elizabeth is no longer with us. I believe that LE pretty much knows who was behind the abduction and feels that Liz is almost certainly dead. I think they are still trying to build a case but with Ricci gone it is going to be difficult unless they find the body and even then if too much time has passed it could end up like the Chandra Leavy case.
They want other people to give up their time and search for Elizabeth, while they go on vacation. If they believed Elizabeth to be dead, how can they continue to ask strangers to look for her.
I don't care if the police told me she was more than likely dead or not. There isn't any body. Until Elizabeth comes back or her body is discovered, there would be no closure.