A cruise ship is a small city. Anything that can happen in your home town can happen on a ship. However, while I have no statistics, I suspect the crime rate is much lower on a ship than in most cities.
Medical emergencies can happen at home, at work, at the mall, at a friends house, or while you are on vacation.
As my screen name suggests, I work in TV. My first cruise was in 1980 and I was a photographer working on a week long series of stories on the cruise ship Mermoz out of Miami. This was when the Love Boat was the number 1 show on TV. By Maritime law, every cruise ship above a certain passenger capacity must have a medical facility and mortuary facilities. I did not tour the Magic's health center, but I suspect somewhere there are facilities for storing a body or two in case of the unthinkable. Disney's passengers on average are a lot younger than many other cruise lines, but I know back in 1980 on the Mermoz they said they had about 6 passengers a year pass away on board. Mind you too, their passengers were even older than the norm, and while it was a smaller ship too, 450 passengers, it did only longer cruises, 14 days, and catered to a richer older cliente. The fare for the very small (by Disney standards) cabin I had was $5000 per person for 14 days in 1980 dollars.