Unfortunately, that info is not exactly correct. It is problem as the cruise line can get fined as mentioned in another post. However, if you go to Guest Services and claim an emergency at home, then they can try to get approval from CBP so they do not get fined. I definitely would not proceed there immediately as if it was pre-planned as it could be denied. The form you have to sign says you have to pay the fine if CBP decides to issue one. At least it used to.
By the way, this info is from upper management in Port Operations with MSC Cruises USA, not a random employee trying to get you to book a cruise to get their bonus.
Bret