An interesting topic.
Here is a link to the Quaker document
I have not yet read the entire document, but early on they explain their meaning of the phrase which comes out of a religious context (unsurprisingly):
Our title, Speak Truth to Power, taken from a charge given to Eighteenth Century Friends, suggests the effort that is made to speak from the deepest insight of the Quaker faith, as this faith is understood by those who prepared this study. We speak to power in three senses:
To those who hold high places in our national life and bear the terrible responsibility of making decisions for war or peace.
To the American people who are the final reservoir of power in this country and whose values and expectations set the limits for those who exercise authority.
To the idea of Power itself, and its impact on Twentieth Century life.
Our truth is an ancient one: that love endures and overcomes; that hatred destroys; that what is obtained by love is retained, but what is obtained by hatred proves a burden. This truth, fundamental to the position which rejects reliance on the method of war, is ultimately a religious perception, a belief that stands outside of history. Because of this we could not end this study without discussing the relationship between the politics of time with which men are daily concerned and the politics of eternity which they too easily ignore.