Is the validity of the ransom contingent on Jesus being God?

In discussing the trinity, I've often heard people say that "only God could perform the ransom" or that "only the creator of life could defeat death." What is the basis for these claims? To give some context, non-trinitarians, such as Jehovah's Witnesses, believe that Jesus was a perfect man in the same manner as Adam, but Adam was not God, therefore the ransom doesn't necessarily need to be by God, but it does need to be by a corresponding perfect man. (Romans 5:12-21; 1 Timothy 2:5, 6 ) What is the basis (Biblical or otherwise) for believing that Jesus must also be God in order for his ransom to be valid, especially within the framework of the [Recapitulation theory of atonement](https://en.m.wikipedia.org/wiki/Recapitulation_theory_of_atonement) ?