Remember that Beth Holloway was with Greta, and the two of them went in and spoke to both wife and Paulus for about 90 min. That was meant to bring the two upset families together, not meant to be an outright interview with the parents.
So Greta probably said something like, "I want to give you both opportunity to present YOUR point of view, just as I gave the Holloways that chance in my interviews with them." And they went for it.
I was wondering if something he said during that first talkfest might have been told to the police and they cross-checked it with what he had told them, and something did not match up, even BEFORE the latest interview with the two.
You're right about Greta's cleverly maneuvering the vdS's into that second interview. As for Papa v.d.S, when you lie, it's just about impossible to keep the lie going. You tend to embroider, embellish, and then can't keep anything straight. No wonder he was sweating and wringing his hands. And that terrible moment caught on tape when the camera zoomed in on the sweat trickling down his forehead. He didn't dare take out a handkerchief and wipe his face!