I'm pretty sure a cruise with a foreign port on its itinerary counts as leaving the country whether you disembark or not.

This is actually a very good question. I have some friends leaving on a cruise this weekend, two of which are on H1 visas and do not have entry documents for some of the foreign ports. The cruiseline told them they will need to remain on board and cannot disembark.

Upon arrival back to the US, will CIS consider they left the US and/or entered another country, even though they remained on board the entire time?

Is it also possible the cruise line rep gave them incorrect information and they will be prevented from boarding the ship without valid travel documents for the various ports they are stopping at?

Correct. In cases like this you will need to do customs even if you plan to stay on board

Cheers

Right. The issue is the Passenger Vessel Services Act. This act prohibits foreign vessels from transporting solely between US ports. Since almost all cruise ships are registered in foreign countries, if they stop (or start) at any US port, they have to visit at least one foreign port. That's why NCL flagged one new ship under the US flag (with at least one more on the way). These will be dedicated to cruising Hawaii.

I don't know if boarding one of the NCL ships is considered leaving the US, but certainly boarding any other ship is. You have to have all of your documents in order prior to leaving. There are no provisions to prevent a passenger from leaving the ship at one or more specific port(s).

BTW, did you know that cruise ships recommend that passports are NOT taken off the ship when you leave in a foreign port? Your cruise card/boarding pass or whatever the specifc cruise line calls your ship-assigned ID card is all you should take on shore. At least that was what was told to me at European, Caribbean, and Mexican ports.

When we were on a US cruise ex FLL, all passengers who did not have US passports had to leave their passports with the cruise line when going on shore.

Cheers