Law enforcement often employs archaeologists for that very purpose. My professor in Uni for example would go help them out whenever they got a call about a body being found because there just weren't enough murders in my part of the world to justify having someone full time.
The skill-sets are virtually identical, the bones are just fresher. Reading a crime scene and reading a archaeological site are basically kissing cousins.
Well, a court ordered exhumanitions of a murder victim is not grave robbing, so your example in the 2nd paragraph just makes the point that there are in fact more categories than "grave robbing" and "archeology".
And yeah, governments often definite who owns what (since in natural terms, plenty of things such as land cannot be possessed) and hence directly or indirectly what is robbery.
(Which brings the interesting question of "who owns the grave" so that taking from it is robbery).