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I am very surprised that there is any confusion among English speakers regarding 'channeling Churchill'.
It is almost an idiomatic phrase to be 'channeling Hitler' if you are spouting insane bigotry or 'channeling Ghandi' if you are advocating peace or 'channeling Bush' if you make no sense at all.

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Channelers are charlatans who deceive the dupable out of dollars by pretending to channel or act as a conduit for the spirits of the dead to converse with the living.
The channeler claims to be like a water course simply directing the flow of the information but taking no part in the conversation. Yeah right!