Hi LaurLaw and welcome...
It appears you have some legal background. I have to warn you that once you get started in looking at Maritime law you may become addicted to studying it.
You may be correct in your assumptions, and in this case the cruise fare was low enough that a small claim court could settle it. (making it possibly simple to litigate).
I can tell you this, were you (as a lawyer) to write a letter challenging the decision their reply would be a copy of the cruise contract which the guest signed when they bought the cruise. Among other stips the contract says the cruise line has the right to refuse the cruise for any reason, including failure to go to life boat drill, fighting, arguing, using foul language, etc.
The jurisdiction for cruise ships is the nation where the vessel is flagged (often Bahamas, or Panama). The contract says the cruise line must be sued in the state where the head company is incorporated (in this case Florida). Local laws do apply if a ship is within the territorial waters of any given state (up to the 12-mile limit) but outside of territorial waters the jurisdiction goes to federal officers (the FBI) and courts (Federal Maritime court).
As you know, there is no such thing as "international law" although maritime law is largely regulated by various treaties which most nations have signed. One pending treaty (since at least before 2000) which the US has not signed yet is the LOST treaty (Law of the Open Sea Treaty). It is doubtful we ever will sign it since it limits access to "international" waters up to 200 miles unless given permission, and a number of other factors the US feels would impede military matters.
Most civil matters in these treaties have to do with crew members, more so than passengers.
Regarding the medical facilities. Cruise ships have them as a convenience, not as an official medical facility. So, it cannot be forced to take care of anyone. One could argue that they then also could not deny a cruise, but they don't, the cruise line (and/or captain of the vessel) do that, under the advice of the doctor.