Well, I'll take a stab at why this case holds such "fascination", if that's what it is: How many of these overboards are still active investigations within the FBI many years later? How many happened sans any evidence, such as a witness, someone hearing a scream, scuff marks on rails, etc.
How many happened exactly at the time when a kidnapping would likely occur -when the ship was in docking procedures?
I've read about several cases over the years of people going overboard, but never one like this. Many accounts, from different people, of strange happenings surrounding the disappearance, including missing cruise photos (all photos of Amy missing, but none of anyone else). A record of the missing person complaining about "creepy" people who had expressed interest in her.
Here is the crux of why I find this case so compelling: The patterns. The story. One can lay it all out chronologically: Amy goes on a cruise and meets, dances with, a guy who many end up characterizing as "creepy". Amy is "partying", out having fun and, as such, likely off her normal, day-to-day "guard".
Parents feel that the attention given her is odd. She, herself, complains about them. She's seen very early, as the ship is starting docking procedures, accompanied by the guy from the night before, who "gives her something to drink - a dark liquid". They're both seen going up in the glass elevator to the disco floor, but only one is seen coming down. There is a freight/staff elevator behind the disco which, conveniently, is not glass.
As the boat is docking, Amy becomes missing. Then, there are the sightings. They are mostly in and around the Caribbian, with the exception of the SF sighting. Even that sighting, though, is taken very seriously by the FBI, and seems to involve some of the same "handlers" identified in the other sightings. They are all within a few months to a few years after the disappearance, and witnesses describe details that haven't been released to the public, such as the watch and tattoos. A few years later -again, within months to a few years after the disappearance- a professional analyist determines that she is, indeed, the adult escort pictured on a website. (Except now with long, permed hair.)
Yes, people do go overboard on cruise ships. The chances of it are incredibly low, considering the millions of people who take cruises every year, but it does happen. I can say; however, that I've never followed any of the other cases because they seem to be just what they are: Someone who fell, got pushed, or committed suicide.
Really, is there another story out there like Amy's?