Exactly! If your idea here is correct, then they wanted help from the cops. (So they downplayed the possibility of her being a runaway.) If they were hiding some secret knowledge, that one of them had murdered her or sent her away, they wouldn't WANT any help from the cops. If they didn't want any help from the cops, that, to me, would have pointed towards guilt on their part.
Are you typing that with a straight face? Of course none of the family is guilty of the actions you mention. That would NOT be why she disappeared.