Well assuming you are the only one there, you would not be assembling. And thus not need a firearm, unless you truly intend to shoot fish in a barrel.
I have never been to NC, so I have no idea how widely oc is accepted there, but I do not think it impossible for you to receive unwanted attention.
However, this seems like a law that not many people would know/research, chances are if someone is calling the police it will be for a man with a gun.... and not.... a man with a gun in a place that charges a fee to assemble.
But honestly I think your girlfriend is WRONG, if, and only if you can enter the pier for free if you did not want to fish. Then you would be able to make the case that since the fee is only assesed to those who wish to fish, that this fee is to cover the piers fee for holding a public license, and not for admission thereto.
Anyone else think the same?