> finding it in a context where you can determine the date and place it was dropped and who might have owned it is valuable information that doesn't usually follow black market artefacts around (because it's proof of a crime)
Is it? I'd guess that that sort of information doesn't follow black market artifacts around because the black market is just generally shady. I'd expect that any evidence of crime would quickly wash out, for the following reason:
I recall reading a post on Language Log (here: http://languagelog.ldc.upenn.edu/nll/?p=4120 ) about finding a cuneiform tablet at an "estate sale" in Seattle. The author brought it to an expert on the ancient near east and was surprised to have it confirmed as genuine.
There were indignant comments on the post, to the effect that obviously nobody in the US could legitimately own a cuneiform tablet from ancient Mesopotamia. So why wasn't this guy violating the law? And the very sensible answer was that a law prohibiting the ownership of old objects would mainly have the effect that people fearing discovery would destroy their antiquities, simultaneously removing all evidence of any putative crime and preventing anyone from ever learning anything from what used to be a (semi-)valuable artifact.
It's harder to destroy a metal coin than a block of clay, but most artifacts, like bones, statues, and inscriptions, don't pose such difficulties. Is it really illegal to own an old coin while not being illegal to own an old document?
edit: rereading the comments, it seems that owning these old things frequently is illegal, although interestingly owning the same item might or might not be illegal depending on the details of how you obtained it (not the details of where it came from). But I'll leave my comment up because I think the ideas expressed have some merit, although they don't entirely source to the comment thread that I "remembered" them from, and are a little more hypothetical and less factual than I originally thought.