I may be reading this wrong, but it sounds like the Italian government is saying, “We looted this from Greece, therefore it is ours!” I certainly don’t know the details surrounding international laws about pulling up antiquities from international waters, but I really don’t see the Italian governments claim on the work.
What, you thought Southern Californians deserved the privilege of having a comprehensive collection of Classical sculpture in their back yard? Or for that matter, Americans generally? There was a case a few years ago in which Italy was trying to get something back that had been at the Metropolitan for a hundred years. I don’t think they succeeded, but who knows what’ll happen in the future. The title on nothing is safe, and the day may come when we will only be able to look at these things in books, short of traveling to Europe, and our (Southern California) museums will have no antiquities besides local native artifacts.
As for the specifics of this claim, I don’t quite understand it myself. The work appears to be Greek, but Italy claims it by right of (its fishermen) having brought it to light? How is this stronger than an American museum paying good money for it?