A strange thing happened on Summit, after we left San Francisco en route to Catalina Island in Sept. We departed SF on sked at 6PM. While having dinner, about 9PM, there was an announcement that the ship had turned around and was returning to SF for an "Emergency". We arrived back at SF about 11:30 PM. A woman was taken off in a wheelchair, together with a man. There was no ambulance. We then departed SF again at midnight, and we arrived at Catalina on time two days later.
Apparently the woman attempted to assault another passenger at her table, and this was not the first time. The line decided to remove her from the ship, hence the return to SF.
Question: Due to the cost of sailing an extra 12 hours, would the line attempt to recover these costs from her? Can you imagine the charge on her credit card!!!
If the vessel arrived in her next port of call on time, how did she sail for an extra twelve hours?
That said, all cruise lines have to build slack into their schedules for possible emergencies -- partly because response to a distress call is not optional under international maritime law when a vessel is at sea and partly because sea conditions or other situations may arise that temporarily prevent a vessel from maintaining full speed. As a result, cruise ships usually operate at less than their top speed and additionally may arrive in ports of call a few hours early when they don't encounter delays en route.
In the case that you described, the ship probably did burn more fuel to arrive on time at the next port of call. It certainly would be just to charge the cost of that fuel to the passenger's shipboard account, but most cruise lines probably do not do so because it's already factored into the normal make-up associated with delays in general. There's also a legal argument that the decision to return to San Francisco to disembark the offending passenger was a matter of the cruise line's discression and thus that the cruise line should absorb the cost of its own decision. It probably would cost the cruise line more to defend a lawsuit than the dollar value in question.