Some excerpts from a piece in the New York Times which gives a very good idea of how complicated all the issues of the Museum Case are:

[...]

At the Rome meeting, Italian officials presented the Getty with evidence to support their claims, and in recent weeks they have begun to show impatience that the Getty has not yet made a formal response. Meanwhile, in a heralded pact, the Metropolitan Museum of Art in New York agreed in February to relinquish title to 21 objects that Italy asserts were looted. In exchange the Met is promised special long-term loans. While stressing that the Getty's staff and lawyers are nearing the end of their review of Italy's claims and that he is moving forward with Greece, Mr. Brand offered no timetable for a reply to either country. "These are very complex issues," he said. "When you look at our list of 52 objects from Italy, there are a whole range of situations."

One of the disputed objects, he said, is a stone torso of a young woman, a kore, that has been claimed by both Greece and Italy. (The Getty's own catalog identifies the statue as probably coming from the Greek island Paros.)

Another is a portrait head that some scholars think is a fake. And even in cases in which the evidence appears to be clear, he said, there are complicating factors.

Much of the evidence consists of photographs of looted objects seized from the archive of Giacomo Medici — a dealer who was convicted in 2004 of antiquities trafficking in Italy — that match objects at the Getty. Documents show that Mr. Medici was in contact with Ms. True, the former curator, and passed on a number of illicit works to the Getty.

But in the case of an Etruscan terra-cotta antefix, or roof ornament, installed on the ground floor of the Getty Villa, Mr. Brand said that a photograph seized from Mr. Medici was only a partial match. The photograph shows the bottom half of the antefix that is now in the museum, yet is paired with a different top half that was never acquired by the Getty. The Getty's top half does not appear in any of the photographs.

"So what do you do?" Mr. Brand asked. "Break it apart again and send them half?"

[...]

For a museum that has only just opened as a stand-alone antiquities center, the quality and quantity of objects demanded back by Greece and Italy could seem deeply threatening. On a recent visit a reporter was able to identify in almost every gallery objects that appear on the Italian and Greek lists, ranging from a small stone statue of Tyche, the goddess of fortune, to a pair of remarkable red-figure Attic vases with scenes of athletes, to a painting-size fragment of a Pompeian fresco.

Among the works sought by Italy is a marble ceremonial basin, or lekanis, depicting in color — and surviving examples of painted stone are a rarity — a scene from the Iliad. Ms. Wight described it as "the only piece of its kind."

The Greek and Italian claims have lent ammunition to archaeologists who say that the Getty's collecting practices are an incentive to looters and have erased the archaeological context of countless artifacts.

Mr. Brand counters that by bringing a bit of ancient Rome and Greece to Southern California, the Getty has performed a great service to the public and to scholars.

"I think if you look at Marion and at the Getty Museum, I don't think you could ever accuse us of not using objects to good ends," he said.

FWIW, something which is increasingly bothering me about the 'mantra' of 'encouraging looters' and 'lost context' is that none of the players who chant it, be they Italian officials, Greek officials, the AIA, or whoever, can offer any assurance that 'another system' (whatever that may be ... we are never told of what the alternative is going to be) will 'solve' the problem. Increasingly it seems this whole thing is about getting stuff back rather than preventing more stuff from appearing in private collections.