Try separating the process from the desired outcomes.
It probably works like this:
US: "We've picked up this guy, says he lives in UK. What do you guys know about him and what would you like us to ask him"
(UK responds to the request)
Later. US: "OK, we've talked to him at length and he has told us XYZ - want to know what he told us?".
UK: "Yes, please".
Does that make the UK a conspirator to torture? I don't think so.
We all know, surely, that politicians (and many other walks of life) have ways of distancing themselves from events that might bite them - some more successfully than others.