There is some confusion in the post I linked to about the specific source of the phrase "plausible deniability" in describing the LDS church's master-minding Prop 8 and "respectable distance" in the same context. The post I linked to said that this was a quote from a document. It now appears from the full trial transcript that it wasn't. It was a quote from a plantiffs' witness' characterization of a Mormon document, as in the following exchange (PDF Pages 1628 - 1637):
Q. As a political scientist, what is it about this document and these statements that is relevant to analyzing the balance of political power between gay men and lesbians and religious organizations to the extent they're involved in political activities in California?
A. Well, with respect to the Proposition 8 campaign, it makes it clear that there was a sort of two-way flow of information, where strategic talking points were being provided to religious leaders by the campaign. And, in turn, the religious leaders were providing volunteers to the campaign. But there was this cautious strategic not-to-take-the-lead notion so as to provide a -- I don't know, plausible deniability or respectable distance between the church organization per se and the actual campaign.
Here's the actual quote from the document the witness was interpreting:
"He has also been hired by the coalition to do polling work for Prop 8. The main California grass roots leaders are in the process of being called as, quote, area directors, end quote, with the responsibility for areas that generally correspond to each of the 17 LDS coordinating councils for the LDS mission boundaries. Thereafter, priesthood leaders will call local prop coordinators over each stake and leaders by zip code within each ward - potentially working not only with LDS, but also LDS volunteers."