They are not asking for direct payment. They want me to pay the collection agency. I am not going to make an international payment to some random company that I have no idea about. I suspect they want me to do this because closing internally with the company will mean admitting to the agency that they sold a bad debt.
What a stupid suggestion. If a company cannot be trusted to fix a simple billing issue, I sure as hell wouldn't trust their choice of random foreign company that for some reason they want me to send money to to fix their mistake.
This screams of dodginess and shoddy unfriendly customer service.