Say "Yes absolutely, you giving us those names grants you full immunity." Once he has given those names just send him to jail. He's okay with lying to the public why wouldn't it be fine to lie to him? He has ruined a country when the country needed him.
I think they were freezing and somehow got incapacitated. Thankfully they had a whistle, so they blew into the whistle and someone heard it and came for the rescue. I think that may be the story.