In Crete you may get driving accidents, people driving off cliffs, people shooting each other accidentally (Crete is the only place in Greece where guns are not exactly allowed, but turned a blind eye to) or even vendetta-type shootings between families as revenge for insults (like you get in many parts of the Mediterranean, though such killings are on the decline with younger generations) but these happen "in the open", they don't hide corpses away in caves. You definitely don't get serial homicide or the type of crime you get in a big city. It's a rural place with very rich agriculture. Some of that agriculture may just be a little illegal. Hence, perhaps, the burlap.
However the situation is different in the big cities, where you get all kinds of criminal activity and there is very widespread interest among the public, with shows on the TV etc. Despite that, the police usually tend to keep quiet until cases are solved. So this kind of silence is normal, and usually seen when they are close to solving a case.