I'm struggling with why he would
single out the green shed as the location of the rape unless it's actually true.
(and we have mostly, I think, been assuming that the real attack did take place in the park). Admitting to a park location would make his claim that he left Libby alive, and the implication that she must have either deliberately or accidentally made her own way to the river, more plausible - he could have claimed that she refused to leave with him, for instance, so he had to leave her. Singling out the green shed makes it harder for anyone to believe that Libby walked away from the lights and into the darkness of her own accord. So, why lie about the location in a way that weakens his own case? Or, by giving that location, is he perhaps banking on it making the timings to and from the river even tighter? Yet the defence haven't (so far) queried the timing element of it at all - presumably because if their case is that he was not in the park at that time, the timing interval of how long to the river bank etc is irrelevant?
I think there may be a grain of truth in the rape location if nothing else. He may have struggled to 'contain' himself for long enough to get Libby into the park. We know how badly incapacitated she was, but he didn't necessarily know the full extent of it; he may have though that he didn't stand a chance of getting her into the park without a struggle, and opted for right outside the car instead. If Libby ran from the car and he immediately caught her, this location would also make sense - for rape, but not necessarily for the murder charge. If this location IS true, then it gives rise to more questions than answers about what really happened. If it ISN'T true, then I don't get the point of the lie.