The theory is called in rem jurisdiction. The same theory is used by the federal government in criminal forfeiture actions. You acquire jurisdiction by suing the asset which lies in your jurisdiction. This is a common maritime practice.

Carnival is ordinarily allowed to post a bond equal to the price of the cruise ship and the res (property) will be released. The problem is that Carnival probably doesn't own the ship. The engines (like an aircraft are probably leased), the ship builder has a note on the boat, and Carnival has probably pledged the ship as collateral on various notes. (This common place). I'm not sure whether an in rem action would defeat these secured interests or not. In federal forfeiture law (which is maritime based), it does trump secured filing interests much of the time. It really doesn't matter, the seizure will probably force Carnival to deposit are large pile of cash or promissory notes into the custody of the US Courts to get their ship back.

Cruise Ships are usually registered in Panama, the Bahamas, or Libreria and engage in the legal fiction that they are not subject to US jurisdiction. They do this to avoid labor requirements, tax law, and to a lightly lesser extent tort and liability laws. (That is also why their cruises have at least one non-US stop in all they cruise runs, e.g. (a Pacific coast cruise always includes one Mexican or Canadian city)). The attorney suing them knows this and has taken this move to force them to the table.

I find this legal move by cruise ship companies troubling. When one of their ships get attacked by pirates or is seized by hostile nations. Then they claim they are really American and ask for US help. I think they should be reduced to appealing to the Panamian, Bahamian, or Librerian navies.

I expect that Carnival will offer some form of compensation to their customers for this inconvenience, but as I recall the terms and conditions of their agreement actually exclude this liability as well. This clause is lifted from a Norweigan Cruises (A Bahamian Company despite its name) contract:

"(a) Risk of Travel: The Guest admits and acknowledges that travel by ocean-going vessel occasionally presents risks and circumstances that may be beyond the ability of the Carrier to reasonably control or mitigate. The Guest's understanding includes all risks of travel, transportation, and handling of Guests and baggage. The Guest therefore assumes the risk of and releases the Carrier from any injury, loss, or damage whatsoever arising from, caused by, or in the judgment of the Carrier or Master rendered necessary or advisable by reason of: any act of God or public enemies; force majeure; arrest; restraints of governments or their departments or under color of law; piracy; war; revolution; extortion; terrorist actions or threats; hijacking; bombing; threatened or actual rebellion, insurrection, or civil strife; fire, explosion, collision, stranding or grounding; weather conditions; docking or anchoring difficulty; congestion; perils of the sea, rivers, canals, locks or other waters; perils of navigation of any kind; lack of water or passageway in canals; theft; accident to or from machinery, boilers, or latent defects (even though existing at embarkation or commencement of voyages); barratry; desertion or revolt of the crew; seizure of ship by legal process; strike, lockout or labor disturbance (regardless whether such strike, lockout or labor disturbance results from a dispute between the Carrier and its employees or any other parties); or from losses of any kind beyond the Carrier's control. Under any such circumstances the voyage may be altered, shortened, lengthened, or cancelled in whole or part without liability to the Carrier for a refund or otherwise."

If Carnival wants to be jerks about it, they could simply tell the guests we are sorry, but it is not out fault. We were prepared to give you the cruise but those evil meanie lawyers screwed you out of your vacation. Take the issue up with them and have a nice life.