哪位大俠給我出出注意 refinance

一個小問題，就是有點鬧心。I am co-signer of my cousin's student loan(10k). He paid it off just before I started refinance a month ago. So my credit report shows the loan account is "unrated" instead of "current paiding as agreed".
So the lender asked for the term of loan. I sent a letter from the bank indicated the "loan is satisfied". I thought it's done. However lender asked for "papertrail of loan payment". What?? why?? They want my cousin's bank statement to show the payment transactions. OK My cousin sent it but blocked all transactions except loan payments.
Today my loan agent told me lender is VERY picky and most likely won't accept it. My cousin is unwilling to give full statement.I think I can push him a little hard... but at the same time, I think lender's request is unreasonable. So I want to hear from you guys. Any suggestions or comments? Many thanks.