The concept behind this was that 'sovereign' wrecks (ie. governmentally owned or chartered) remain owned to protect as graveyards and memorials. If the late Mel Fisher, salvor of the Spanish "Nuestra Señora de Atocha" (1622), were to discover the ship today it is probable he could not have salvaged it without the cooperation of the Spanish Government.
In international waters it becomes more dicey as not every shipwreck is readily identifiable. A US Treasure Hunting company, Odyssey Marine, is in legal battle with Spain over treasure recovered from the international waters in the Atlantic known as the "Black Swan Project". The number of governmental 'toes' being negotiated is enough to make you wonder if anybody other than lawyers will win in the end of this case.
“In 1998 the US Courts ruled on 2 Spanish shipwrecks in Virginia waters, Juno (1802) & La Galga (1750), that they remained Spanish ownership because the Spanish Government had never abandoned ‘title’.”
What is being said here is that U.S. shot itself in the foot again.
One may mention (although it is implicit in your post) that this has very much to to do with greed - greed of the various states/governments. For instance Spain which is so keen to protect its national heritage on international waters, "strangely" enough also claims ownership of the British wreck HMS Sussex that lies off Gibraltar in international waters.