Seller is asking to use different lender after low appraisal

[Samuel Brian McKenzie]

I'm under contract for a property, about two weeks from closing. The appraisal came back $18,000 under the agreed-upon price. My contract states that I can back out of the deal if the seller doesn't lower the price to match the appraisal. 

The seller told my real estate agent that he's willing to pay for another appraisal and that he would match whatever price it appraises at the second time or the current agreed-upon price, whichever is lower. He's willing to put that in writing. I would have to use another lender, but the lender would match or beat the rate I'm currently getting. 

This sounds iffy to me, but logically it makes sense and my agent says he think's it's a win/win. Is there any way I can lose from this? They aren't willing to go down to the price of the current appraisal right now so if I don't agree the deal will fall through. 

[Jacob Sampson]

Assuming it is a legitimate appraisal and the seller is paying for it and will extend the closing date then it wouldn't bother me.