No group of fans, no matter how well-intentioned and serious-minded, owns “worldcon.” (Note lowercase “w.”) The word “worldcon” has been part of the fannish lexicon for nearly 70 years and, while the World Science Fiction Convention may want to trademark a “Worldcon” logo or the like, the use of “worldcon” in lower-case in a context unrelated to the World Science Fiction Convention or to any similar convention is part of every fans cultural heritage.The short answer to that assertion is, "You're wrong."
The slightly longer answer involves suggesting he apply that theory to Coke, Kleenex, Xerox, and the Oscar and see how well it works out. Just because those registered marks belong to Big Corporations and Worldcon happens to belong to an unincorporated literary society whose roots trace back to the same corner of fandom of your own doesn't mean it's any less true.