The big is this: was the private tour affiliated with the cruise ship? Even if the cruise ship just recommended the tour, they might be liable.
No, and some think that’s why the cruise ship made an example of them, to discourage passengers from doing tours with unaffiliated parties.
A private tour is not affiliated with the cruise line. If they were on an official shore excursions the ship will wait. That is why ship board excursions are more expensive.
Private tours are never affiliated with the cruise lines. If they had booked their tour with the cruise ship and the tour was running late, the ship would have waited. The rules are made clear. Also, the ships need to leave the ports by a certain time, no exceptions.
“Even if the cruise ship just recommended the tour, they might be liable”
The only tours the cruise companies recommend are those that they sell tickets for.