So you meant they can pass laws outside their borders to make convictions more secure, or that in theory, all US law applies to all US citizens at all times? Sorry for being dense.
Skip to the end for the only sentence in this actually relevant to this specific case because this is kind of autistic and tl;dr.
Usually there are enabling statutes like the one in that DoJ link, and usually, the DoJ is not going to go beyond those. They don't want to be prosecuting every single little crime some American commits as a tourist when the locals are entirely capable of taking care of it themselves.
There's jurisdiction as it exists under international law, which America is pretty cavalier about directly obeying, jurisdiction as far as the Constitution allows, which
theoretically gives the feds jurisdiction over any foreign crimes, statutory jurisdiction, which is where a statute actually grants the jurisdiction to the federal authorities (which is considerably more narrow than the theoretical limit), and sometimes a final layer of statutory jurisdiction which explicitly grants jurisdiction over a specific subset of crime (like the sex tourism statute allowing the punishment of pedophiles abroad as well as people who violate sanctions and a handful of other things).
Usually, you're going to see all four before the feds prosecute an American's misdeeds abroad.
If this sounds complicated, it's actually such a gross oversimplification as to be wrong if you look at the millions of exceptions. But there are entire treatises just on the subject of jurisdiction and we really don't have time for all that.
In short, though, the U.S. probably had the authority to stop this, or at least revoke Stockton's ability to have any operations in the U.S., and possibly prosecute him, even before the disaster. There are probably international authorities with some jurisdiction over the Arctic that could have rejected this "ha ha they're not passengers even though they're paying they're crew yeah that's the ticket" bullshit and revoked any legal authority.
They really should have. It might not have stopped him from doing it anyway. But even on the high seas, we aren't in the age where nothing but piracy and slavery made you
hostis humani generis (an enemy of the human race) who can be attacked and killed by anyone for any reason.
You're generally supposed to be operating under the flag of some country, and subject to its laws, to be lawfully using the oceans.
Also the U.S. has specifically claimed jurisdiction over at least the salvage operation of the Titanic, according to NOAA.
Since 1994, the United States District Court for the Eastern District of Virginia has exercised admiralty jurisdiction over the salvage action brought by RMS Titanic, Inc., the U.S. company that has salvor-in-possession rights to the Titanic wreck site.
I'd consider this a commercial use of the wreck site and probably the proper jurisdiction under admiralty would be the Eastern District of Virginia.