"This aspect of identification, whereby one can protect an interest merely by using terms not incisive enough to criticize it properly, often bring rhetoric to the edge of cunning" (p. 36). Burke gives an example of politicians doing this, but he also brings up that "Whatever the falsity in overplaying a role, there may be honesty in the assuming of that role in itself; and the overplaying may be but a translation into a different medium of communication, a way of amplifying a statement so that it carries better to a large or distant audience" (p. 36).
I think he is saying that if we use the rhetoric as persuasion, even if we are seemingly against what we are supporting, we might actually come to believe it, and we aren't even being dishonest. It may appear that the politician cares for his or her constituents, and in fact, the politician may care a litte, but act like she cares a lot. Burke says that she is not dishonest, only carried away with the role in an effor to have the message heard to a large audience.
You'll probably think I'm pretty naive here. Although I do not, generally, trust politicians, I never felt like many were blatantly lying through their teeth. Unfortunately, as I type this, I'm thinking about former President Clinton. When he lied about what's-her-name, he was not feeling rhetorically dishonest, if you look at what Burke says.
I picked the quote about "terms not incisive enough" because I think about the language we use that is not very clear. Politicians or people in general talk about ideas so abstractly without grounding the ideas in concrete examples that a debate turns into a swirl of words where nothing gets accomplished because you can't really put your finger or argue what they say because there really is no substance. I thought of Hayakawa.