No they don't. Port security has various areas, divisions and dimensions. It is shared by the Coast Guard, Customs and the shipping/maritime company that controls the port. That is what P & O has bid nearly 7 billion dollars to do, control the six eastern sea ports involved in the bid.
But if it makes you sleep better at night, then go on believing the nonsensical notion that the Maritime/shipping companies who are paid to control the port entries really have nothing to do with port security. And you can believe in Peter Pan too.
"DPW would not be responsible for cargo screening, which is performed by the Department of Homeland Security, but the port operator is responsible for securing cargo coming in and out of the port, the port facility itself and the hiring of security personnel."
http://www.foxnews.com/story/0,2933,185107,00.html