Your 3rd point was the big issue sticking out in my mind when I was tying that up. I guess they could claim that the US has the right to protect US based ships, but I don't know how these things work and whether or not that's a legit claim.
As for whether or not it would fall under the Navy's mandate, I would think that protecting American's at sea would be an appropriate task for the Navy. Getting involved with any private shipping industry definitely has it's issues, but it might be worth some thought for any type of ship involved with humanitarian aid.