In addition to the above data, I searched the website of Stratfor, a publicly accessible intelligence and foreign relations news and analysis site, and discovered that a US Military ship was operating in the Mediterranean during the timeline that we believe the Ghost Boat would have sailed for Italy.

According to Stratfor’s report (login required), the USS Bataan (LHD-5), an 844ft “Wasp-class” amphibious assault ship, equipped with a flight deck for military aircraft, was positioned South-East of Italy on the 26th of June, heading West to a position South of Sicilia; where it arrived one week later. The ship then appears to have turned West and sailed to a position South-West of the island of Crete; where it was expected to be by July 10th.

Although the map is inexact in its plotting of the Bataan’s course, it’s position and heading would have put it in an area which the Ghost Boat would have had to cross in order to reach Southern Italy or Lampedusa (a typical destination for refugee boats).

EDIT: Adding the map showing Naval vessel activity. The USS Bataan is labelled LHD-5.

Further details on the USS Bataan are available here.