Yes indeed, Jim, and a possibility that had not occurred to me.
Interestingly, if you go to the jobs section of most major cruise liners, it is usually emphasised that crew members may not socialise with passengers off-duty, or over and above the call of duty,(especially) if entertainers.
This perhaps doesn't seem to be enforced very well. Presumably such rules exist to protect everyone -the cruise line, the crew, and the passengers. You can't entirely protect passengers against mad fellow-passengers, but cruise lines might be better able to defend their reputations and assist in inquiries if they managed to enforce their own rules better.
I suppose it must be a difficult problem because I'm sure passengers like and target crew members for friendship. I've never been on one, so don't know myself, but I have a young cousin who is a (female) purser on a major line and she has constant trouble with unwanted (and forbidden) passenger attentions, and is very wary of her own safety. One can only imagine the same situation applies in reverse sometimes, especially with 2000+ people on board. With such a population, one could perhaps assume at least one person will be either mad or of criminal intent, at least so far as policy-making goes.
I have also been told, but cannot verify personally of course, that there is a higher than average depression / suicide rate among young crew members on cruise ships - particularly among the catering staff. When my son was a junior chef, I suggest a couple of years ago that he might enjoy a year on a cruise ship - he just asked if I was trying to get rid of him for good...