Of course, on the other hand, there is always the possibility that PR admits picking Libby up, has stuck with the story that she tried it on and he pushed her away, and insists she ran off towards the park. He might even have said he went after her to make sure she was ok and saw her on the bench, but then she kept running and he went eventually back to the car.
For all we know he could have rung 999 there and then and given a statement to the police which, combined with reported screams, is how they knew where to look so quickly after Libby was reported missing.
They've then had him under surveillance while they built a picture of his activity that night (and since) but STILL have no physical evidence that his story is wonky.