Actually, now that I think about it - is the US military or coast guard even authorized to operate in the Mediterranean?
Aside from territorial waters, you don't need authorization to operate in the ocean. It's international waters.
There are international agreements to cover maritime search-and-rescue in certain areas, so that (most of the time) two countries don't just point their fingers at each other and say "this one is your problem", but it's not as if you're not allowed to rescue someone in an area that someone else is responsible for rescuing people in.