Disney claim the Liverpool student was swept overboard by a freak wave.
Notes made by Superintendent Paul Rolle, seen by the Liverpool Echo, suggested Rebecca had been involved in a threesome before her death.
The notes state: "(American woman in relationship with Rebecca) left to get more beer.
"Came back and Rebecca and (male crew member who was in a relationship with the American woman) chatting.
"She came back and all 3 went to (male crew member's) room. (Male crew member) had sex with both. (American woman) left the room again to get beer. Came back and Rebecca and (male crew member) had sex."
The investigator also said the male had a "very nonchalant attitude" and was "laughing and joking" - to the point he was given a warning.
No stormy seas were recorded to support Disney's wave theory, and the Royal Bahamas Police probe has been condemned as 'appalling' by influential MPs.
Mike and Ann Coriam, from Chester, along with maritime expert and family spokesman Bill Anderson, strongly suspect Rebecca was murdered following a sex attack.
They are convinced their daughter, who was working on the ship as a childminder, was victim of a sexual assault in the hours leading up to her disappearance.
Names of the potential suspects, one man and one woman, are known to private investigators.
Two of the Liverpool student's best friends visited the Coriam parents after she went missing, and said their friend had voiced fears of being raped or sexually attacked while on the ship.
Maritime expert Bill Anderson said: "What her best friends said to the Coriams sent a shiver down their spines.
"They told Mike and Ann and they then told the police. We are asking the UK government for an inquiry into Rebecca's disappearance, but also a probe into what the police in the Bahamas never did."
Another theory of suicide fails to fit, the Coriams believe, because the cruise ship worker had recently bought tickets for her parents to visit Disneyland Paris.
The family have the support of many senior politicians including ex-deputy Labour leader John Prescott who has previously alleged Rebecca was "thrown overboard".
Those tickets were found on a table in her cabin when her disappearance first emerged, and was a sign of a young woman looking forward to the future.
The Coriams, Mr Anderson, and Roy Ramm - the former Commander of Specialist Operations at Scotland Yard, and the family's private detective - recently visited policing minister Brandon Lewis at his Home Office HQ in London.
The family left the meeting optimistic, after being assured that the Tory politician would examine a dossier of new evidence about the case, handed to him by the Coriam campaigners.
After nine months, the investigating Bahamas police department declared the 24-year-old's disappearance as "not suspicious".
Disney insist Rebecca, who studied childhood studies, psychology and philosophy at Liverpool Hope University, was swept overboard.
But Rebecca's family think she was probably killed, and in November private investigators disclosed their belief that 'criminal activity' was behind her vanishing.
Chester MP Chris Matheson, who is coordinating the investigation, believes there is a real possibility that Rebecca was murdered.
And that train of events is supported by the allegations of rape or sexual assault, campaigners added.
In 2015 Mr Matheson said: "I believe there's sufficient evidence to indicate a crime may well have taken place.
"Whatever the circumstance, there's an obligation to investigate. My worst fear is Rebecca Coriam was murdered."
- Daily Mail
