OK, just watched Asylum again, and the Daleks' motives for using the Doctor in the Asylum are a hell of a lot clearer once you know that Oswin's a Dalek.
The broadcast of Carmen was done by a Dalek. It was carried by a Dalek frequency. To the minds of the Dalek Parliament, this meant that the insane Daleks had the capability to manipulate the pathweb. As a result, any Dalek taskforce that was sent down to the Asylum was vulnerable to whatever the Asylum Daleks could cook up. They had no idea that the Daleks were dormant and the broadcast was benign. So, they had a force that was capable of stopping any Daleks in their tracks, a force that, as the end of the episode shows, was entirely capable of influencing all the Daleks. Of course they're going to be terrified! If they can't send a Dalek, send the Predator instead, and, if he gets blown up along with the Asylum, all the better.
What I thought was a jarring plothole actually makes perfect sense once you know about Oswin's fate and the pathweb.
