Right in the beginning of Bava Metzia in Tosphots and on page 7, there is raised the issue of when the law is to divide, when "who is stronger", when we say it should remain as it is until Eliyahu comes.

So one of the issues is this a document of a loan is in the hands of a middle man and he has forgotten who gave it to him, the lender or the borrower. There we say it should remain where it is until Eliyahu come.

Rav Shach asks why is this any different from an object that was given to a middle man to help until the people that gave it to him come to get it. And he has forgotten who gave it to him and he gives it to one and pays the other since it was his fault for not writing it down or remembering who gave it to him. 

The answer of Rav Shach I admit is a bit  hard to understand. The document he says has a category of a verbal loan and that makes sense since the only difference between a verbal loan and one in a document is the borrower can say "I paid" in a verbal loan. The written loan he can not say that because the lender can ask, "Then why do I still have the document?"  [So in the case the document is in the hands of teh third party the lender can not say that.] Still it is hard to understand why here also we do not say it is the fault of the middle man for not writing down who gave the document to him.