It’s a sign of the success of “DNA fingerprinting” that any kind of identification technique is immediatly cast in those terms (“DNA-like technique may help nab fossil thieves”). But the method described in the linked AP story is actually a lot more like the “fluorine dating” method that exposed the Piltdown hoax.
Researchers are testing methods designed to match chemical signatures of naturally occurring elements that seep into bones during fossilization with surrounding soil. The process which analyzes a group known as rare earth elements could someday lead to a database of site "fingerprints" used to link bones to looted areas. More work is needed, but early signs are encouraging that the technique could be useful in nabbing those capitalizing on looted fossils, said Dennis Terry, a researcher at Temple University in Philadelphia.
The point is, the absorption or incorporation of elements in fossils at a site are relative to depositional history and local concentrations. With Piltdown, the human skull and orangutan jaw hadn’t been in the site as long as the fauna, which was made plain by the lack of consistency of fluorine concentrations. But it is easier to show gross inconsistency than to prove identity. Even two fossils from the same level at the same cave may have rather different fluorine concentrations, because different parts of a site may relate differently to groundwater fluctuations.
Looking at several rare earth elements may increase the information content greatly, allowing finer resolution, but in the end it is still the problem of establishing confidence. Similar methods help to show that rocks originate with a single volcanic eruption, so it seems plausible that one could do the same for fossils. But it will take a big database to generate sound statistics.