One thing is clear from the return of antiquities to Italy and Greece: the same names pop up time and time again. And those in the know are wise enough to avoid antiquities that once passed through, say, the hands of certain dealers or the halls of certain auction houses.
Who wants to buy an antiquity only to find that it features in one of the thousands of images forming part of the archives in the hands of the Italian and Greek governments? Imagine spending tens of thousands of dollars, pounds or euros to buy a piece of ancient art only to find that it has a more than interesting collecting history. (And who in this time of global financial uncertainty can afford to make that sort of mistake?)
Time and again we have read that museums and private collectors have bought "in good faith" - they never meant to buy looted objects.
That is why auction-houses, for example, need to provide the full collecting histories for objects. It is not enough to check datasets for stolen objects - the staff need to undertake some rigorous checks of their own and then make their findings public. That is what due diligence is all about.