Apparently, this is an old story. But according to the Guardian, it's still going on. I had a quick look at the data to see if anything weird was going on. First I checked whether there were missing imports of olive oil in Italy, i.e. whether oil from Greece, Spain, Tunisia and Morocco was imported illegally in Italy. As seen below, it doesn't seem to be the case, as Italy imports more from these countries than they actually export (in kg). Where these extra kg come from is a mystery, but it could be that exports are not reported properly in North Africa.
I then checked whether imports from Spain, Greece, Tunisia and Morocco actually predicted Italian exports. I find little co-movement in quantities, suggesting the illegal transshipment may not be so important as to appear in aggregate figures. However, Italy imports much more olive oil than it exports. And if we look at trade values, imports and exports seem to move together. I guess this is because Italians consume more olive oil than they produce while their exports almost pay for it all. Nice gains from trade?