LOL the guy is a halfwit. Nobody is posting *anything* to your site. You are merely downloading the newsgroup to your sites server the same way as he downloads the group to his computer. He replies thru his computer, your members reply thru the client of your board. Once posts are on the usenet servers (wherever that may be) nobody can control who gets to download them if they have a feed.
If his ISP decided not to have a newserver anymore (they have to pay for the service) well he'd have to look for a free one or use a service like Google or your site <snerk>
Just point out the facts to him and tell him if he doesn't cut it out not only is he showing himself up to be a fool, but you'll report him for harassment.
He can't win, so don't sweat it.