I didn't see the 20/20 show in question, but I can tell you over the years I have seen incidence of severe drunkeness, and bartenders over serving already obviously enebriated passengers.
I've seen incidents of physical confrontations between passengers; some handled well, others not so well.
The worst was a case of domestic violence, where the ship "official" knew I was onboard as a member of the press, and a partial witness to the incident. They told me the husband was put off the ship in port the following day; imagine my surprise when I saw the man still onboard 2 days later, though his wife did tell me that he hadn't been allowed to return to their cabin.
Frankly I do believe there is a lack of a "security force" on ships these days. Many towns smaller than cruise ships have a police force.
I don't think the incidents of violence and crime are regular occurances on ships. But I do think we need to remember that the cruise industry is in many areas unregulated (self-regulated), and we shouldn't wear blinders just because we love cruising.