Your assessment are correct. The hosts of this game made the mistake of kidnapping them before the family conference, where they were all prepared to get into a tough argument with Natsuhi and her husband. It's no surprise they're still on edge.

[No matter what 'important' means, chances are that Lotus wants them alive no matter what, so he chooses to believe that]

I hold no ill feelings or any particular affection towards those four, but I don't actively want any of them dead. In fact, if it were up to me, I'd send the four of them to the hotel as soon as possible, to save their lives in this game. Mary sending Natsuhi to the hotel was lucky happenstance, yet I can't take credit for it. Their consolation prizes may change their lives to the better back in our world, too.