They didn't think she had fallen overboard though did she?
At the time of her disappearance the ship was just about to dock in Curaçao, meaning it wasn't out in really deep ocean, and it would fairly likely that a body would wash up on shore or be relatively easy to find in relatively shallow waters. She was also a trained lifeguard and very strong swimmer (although she may have still been drunk at the time). Of course that doesn't rule it out though.
Also, her own balcony was one where it didn't just go straight down, it was a terrace of balconies below so I think it would have been impossible to fall overboard from her own balcony at least?
She was allegedly seen at about 6am (so after her dad saw her on the balcony) in the bar with that 'Yellow' guy and he handed her a drink of what looked like coke or coffee?
Yes, I guess she could have still fallen overboard, but it's actually pretty hard to do that, and she would have had to be standing on the edge, the sides of cruise ships are really high you can't just 'fall'.
The other thing that was interesting was that they were talking about the fact that law enforcement on cruise ships can actually be really difficult because of different countries and jurisdictions, and that often no one is actually accountable when something like this happens. It's tighter post 9/11 but Amy-Lynne went missing in 1998 and her parents set up a charity to help get justice for lots of families who have been the victims of crimes on cruise ships or where things haven't been investigated properly.