Winni,
I agree with your approach to escalate this dispute gradually and your decision to follow up to contact "the company" that he is accusing of causing this problem. I disagree with your level of aggressiveness. Even if his statements are true and whether we believe him or not is not that pertinent. You have no leverage on "the company". You have not entered into any agreement with them and are not responsible to fight this individual's battles with them.
There is no reason to delay the exposure of this individual's identity to the public. He is now clearly following this thread and has said he will pay even if the exposure is made. So be it. Let him make his own case directly and if convincing this will allow him to avoid the criticism that he will be facing when his identity becomes generally known. And, I assure you, we will all learn who he is eventually. These things cannot remain secret when so many know who he is already.