Interesting how we see 2 different schools of thought in this thread.
I think it's a case by case basis. You first need to see whether or not he dropped some negative reviews all over the web. If he did, then I would play the eye for an eye game and tell him that you have is name, company and address and can do the same thing unless he removes his reviews that were truly uncalled for. However, if he didn't leave any negative review and you threaten him, that might give him that extra motivation to go on a neg rep spree...
Basically I think you reacted too quickly... you should have just apologized, explained that you just saw his messages cuz you were way, and fully refunded him... then waited a while to see if he'd calm down before threatening him.
Threatening someone shows weakness. By threatening someone you subconsciously admit to them that you are threatened by them, or you would have no need to play the card. There's very few instances where threatening someone results in a better situation. This is not a situation where a threat should ever be used, no matter how far they try to take the damage. You're just giving them more ammo.