All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The authentication of loan by writing it down and having witnesses to it is a desirable act but not an obligation. The majority of Muslim scholars , are of the opinion that the command of writing down the loan and having witnesses to it stands for desirability and likeability. This command applies to every one; a relative, an alien, a lender and a borrower. It does not seem to be an act of distrust, rather it safeguards the rights.
As for the mentioned Hadeeth, we have no knowledge of it.
Allaah Knows best.