http://news.google.com/newspapers?nid=1298&dat=19980327&id=azQzAAAAIBAJ&sjid=4ggGAAAAIBAJ&pg=2506,4843224
The ship was ten miles off shore when Amy
was reported missing.
"The ship was ten miles off Willemstad."
http://www.ctsi.net/amy/
"She was reported missing at 7 a.m., when the ship, the Rhapsody of the Seas, was 10 miles south of Willemstad, Curaco."
The ship was likely farther than ten miles away from shore
when she fell in. But since ten miles is the point where she was known to be missing, let'a talk about ten miles offshore:
Ten miles is in open water; land would perhaps been seen in the distance, or maybe not. Ten miles offshore is a survival challenge if you fall in the water. "Trained lifeguard" means nothing at this point because you can't swim that far and Amy would have known it. If this would happen, you float, conserve energy, float and wait to be rescued. No one on the boat knew she went over and she had no whistle or flotation device. It appears the water was rough as Amy seemed to be seasick. It would also have been dark:
https://www.timezoneguide.com/sunrise-sunset-day-Netherlands_Antilles_Curacao-1-03-513xml.html
Sunrise in Curaso on March 1 (closest I could find to the 24th) is 6:55 a.m. So even by the time her dad discovered her missing (6:15 am ish), it was still dark.
Also remember the water temperature and hypothermia and alcohol vasodilation and dehydration.
http://news.google.com/newspapers?nid=1298&dat=19980327&id=azQzAAAAIBAJ&sjid=4ggGAAAAIBAJ&pg=2506,4843224
"Bradley, a trained lifeguard, may have fallen from the balcony of the family's cabin on the ship's eighth deck, Netherlands Antilles Coast Guard Lt. Sjoerd Soethout said yesterday."
The Fall off the Balcony narrative is there in the historical record if you look for it.