It takes a special kind of warp to claim that you tossed someone overboard because of an accident and then expect to be believed if you already have admitted to lying about dropping her off on shore in the first place. Not to mention that additional grief caused to boyfriend and family by first giving them hope knowing full well that she is dead and then to snatch that hope away again. Asshole.
The most logical explanation that fits all the details is that he killed her and is simply fighting a rearguard action on having to admit that not realizing that his confession is going to end up in the 'optional' bin and that whatever he says will be discounted. Expect to see the book being thrown at Madsen, he's lucky if he gets out in the next decade.