Dealers, where - precisely - do those artefacts come from?

It seems to me that certain US dealers have been claiming that their antiquities are kosher because although they ask-no-questions about the missing documentation, they were bought legally in the EU. When pressed for details we learn they are acquired in in auctions in Britain, Germany, Switzerland and Austria. Now of course we all know that there are 'no' illicit antiquities on the Swiss market, but...

Greek police on Tuesday arrested 26 people suspected of trafficking in antiquities, a police source in the southwestern port of Patras said following a nationwide raid. Six of the arrested were foreigners, the source said, without revealing their nationalities. The police were looking for 15 other people suspected of involvement in the smuggling ring. Initial investigations suggest the gang sold illegally acquired antiquities in auctions in Britain, Germany and Austria. Police raids unearthed ancient statues hidden in a well near the village of Nemea in the Peloponnese region in the country's south. The gang acquired antiquities including ancient coins, valued them and contacted potential buyers in Greece and abroad.

What is the difference between an antiquity which has come from an old collection and has no papers (because somebody never kept any) and one from Kostas the Thieving Digger (who never kept any paperwork either)? Is it really just down to to a dealer's 'gut feeling' ('You've Got to Get That Feeling: Allegedly, the "Right Way" to Collect "Artefacts with Limited Provenance' PACHI Tuesday, 6 September 2016)?

The syndicated AFP newspaper article is illustrated by a nasty stock photo of fake Cycladic figurines and a battered mini-Venus de Milo, all dirtied up.

UPDATE 5th October 2016
A reader (see comments) gave the link to the article in Greek (thanks, Kyri) and suggested we might like to use google translator. I note the following: 

{...] prevented the export of thousands of ancient Greek coins and other objects abroad [...]  the police found and seized: - 2.024 ancient coins, 126 artifacts like figurines rings - earrings - brooches, a bulbous glass vase, five Byzantine icons, a Byzantine cross, two swords, a [column capital].

Two ancient statues, medieval Frankish era, 1.6 metres tall, depicting a warrior man and one woman, w[ere] discovered hidden in a well in Nemea.

these guys were caught red handed smuggling:

Of the total number of findings, 946 ancient coins and 32 ancient objects identified by police of Subdivision Security Patras, the men support the Port Authority of Patras hidden in a car bumper [...] before crossing the Greek - Bulgarian border, with a final destination in Germany.

They also found a lot of guns and other weapons, and 'twenty one metal detecting machines', but also what looks like a lot of stolen stuff ('seventy-three mobile phones seventeen computers - tablets, ten cameras, binoculars' and other stuff Google translator could not cope with. So basically, it would seem from this report that  the German dealers and/or collectors would be buying undocumented finds from armed thieves and putting this stuff on the market (maybe via their 'collections'). What kind of people would be buying from armed thieves?