It's incredibly unlikely that there's anything left that would let us deduce this man's lineage. Given what we know it's dramatically more likely that the aboriginals are related to him than any other group of people.
What I assume you're asking is if the aboriginals really have any right to claim the Mungo Man's remains. Regardless of family relations they disagree that these remains are "property of the scientific community". A lot of grave robbing has happened in the past in the name of archaeology and while these remains were on display at a museum that's not necessarily the most respectful way to treat these remains.
Before I read TFA, I had the same suspicion. This passage indicates that there is at least a cultural connection; that's probably enough:
Two of Mungo Man’s canine teeth, in the lower jaw, were also missing, possibly the result of an adolescent initiation ceremony, and there were the remains of a circular fireplace found nearby. “It took me a long time to digest the implications,” Bowler said. Today, Aboriginal people still use smoke to cleanse the dead. “It’s the same ritual, and there it was 40,000 years ago.”
Keeping the same customs for forty millennia is an amazing accomplishment.
Yes this is strong evidence that Mungo Man is not related to the individuals who now live in the area. The current Australian Aboriginal population is all descended from a single population that appeared sometime between 10-32K years ago [0].
If Aboriginal people publicly dug up bones from random ancient British graves and took them away for scientific study, and the people of Britain objected and wanted the bones back, would you ask the same question?
Mungo Man’s bones weren’t dug up, they were exposed by erosion. If they had not been collected then they would have just turned to dust on the surface.
As for digging up the long dead plenty of non-Europeans are involved in doing this in Britain without comment.
