(They do claim territorial seas around it, but that’s 12nmi instead of 200nmi.)
https://en.wikipedia.org/wiki/Hans_Island
"In 1984, the Danish Minister for Greenland planted the Danish flag on the island and left a little message saying "Velkommen til den danske ø" (English: Welcome to the Danish Island).[12] It is also said he left a bottle of brandy;[12] however, this seems to have been Schnapps,[13] which, unlike brandy, is a traditional Danish spirit. It is commonly told, internally in the Danish Navy, that it was specifically a bottle of Gammel Dansk, which translates literally to 'Old Danish'. The Canadians have reciprocated with their own sign, the flag of Canada and a bottle of Canadian Club.[14]"
So much comes down to natural resources.