Well, in not calling Lockheed's excellent security service, calling the police when ordered not to and inviting round the friends, JR started off the whole pattern of not treating it as prima facie acceptance of the RN would demand.
The biggie, though, would be that JBR wasn't kidnapped. She was murdered in her own home by someone with an astonishing degree of comfort in that home. That suggests some intimacy with the Ramseys. An investigation going in outward circles from the family would presumably uncover them whether you took the RN at face value or not.
Investigators, though, get instincts about staged scenes - the robbery gone wrong springs to mind. I'm just reading about a woman who murdered her husband with some more-or-less untraceable anaesthetic, placed his body so it looked like he had been masturbating while reading Playboy, then set fire to the room with a lit cigar so it would look like he'd had an accident while in the realms of ecstasy. Police accepting this at face value would have absurd. Just as it would have been in the Ramsey case.
