Finnick wouldn't disagree with the impossible part, but the impossible seems to be what's happened here, though he can't understand why, or how, still can't trust it isn't some extra game of the Capitol.

"I don't know if it's real," he says. "But I know enough about being in and around water to know that lake was too cold. You need to let me help you, or things are going to get worse. We need to warm you up."

He holds out a hand to the man again, in a silent appeal, lifting his eyebrows.

That's the problem with hypothermia: when it's bad, the person doesn't want any help. No matter how much they need it.