yup, that's certainly true. problem here is the ownership of the movable heritage, like in the case of elgin marbles, the treasures of troy, the bust of nefertiti, chinese blue-and-white ceramics, etc. so there are legal issues involved.
the world heritage instrument does not really recognized movable heritage per se, like it the case of a british nomination for a ship back in the 1980s, or when it decided to not include the museums found in cerveteri and tarquinia world heritage site as part of the core zone. but if it's indelibly linked to the building/city which is being nominated, it could be an added value to the nomination, such as in the case of "the last supper" by da vinci.