The 1970 UNESCO Convention and Local Laws

The objects returned from North American museums to Italy seem to have surfaced after the 1970 UNESCO Convention. This is in spite of the USA not signing up to the Convention until 1983. (The UK was quite a bit later in 2002.) There are advocates of the 1983 cut off point but the Italian Government has been effective in applying the 1970 deadline. (See "Cultural Ceasefire: is 1970 the right date?")

But some disputed cultural property could have surfaced before that crucial date. Take for example these three examples:

• The Lydian Hoard returned to Turkey from the Metropolitan Museum of Art in New York (see "Bonham's, Lydian Silver and a Code of Ethics" a related piece offered by Bonham's in London in 2007)
  
• The Keros Haul from the Cycladic islands in Greece
• The monumental Roman bronze portrait statues from Bubon in Turkey
  

Can notorious acts of looting be overlooked because they apparently took place before 1970?

Is the 1970 merely a helpful and convenient marker? Is it hard for a museum (or a private collector) acquiring antiquities since 1970 to say that they were unaware of the issues?

And where do national laws on antiquities fit into all of this?

And what about objects that were acquired before the creation of modern nation states?