The plane apparently ran out of fuel as strong crosswinds prevented it from landing on the island’s 1 kilometer-long airstrip, air force chief Gen. Jorge Rojas said.
That seems quite the leap at this stage of the investigation.
Why?
I am sure that the pilot was talking to those on the ground at the airfield, the cross-wind problem would have been obvious (especially if 2 failed landing attempts had been made, as reported in this thread) and the fuel load is known.
It is VERY likely that the pilot informed the ground station that the aircraft was low on, or out of, fuel and what the intentions (attempt to ditch?) were.