"To be honest", for example, is extremely common and doesn't all that often precede lies, despite its face value meaning. Sure, sometimes it precedes a lie, but then, so does the word "the". For example, "Look, to be honest, I really don't know why the server crashed yet, but I'll do what I can to find out." This is a sentence that many who run startups will have uttered at one point in their life without any intention of misleading anyone.
Even the "ultimate but-head" that the author presents, "I'm not saying that...", which he implies means "I'm pretending that I'm not saying that...", is not at all such a clear case. "I'm not saying that X" can and often does mean, very simply, that you want to be clear where your next statement stops. For example: "I'm not saying that the deal is off, but we're going to have to really work on clauses 3 and 4 before we can move forward." or even, more melodramatically, "I'm not saying that you murdered her, I really don't think there's enough evidence to make such a case at this point, but the evidence really doesn't look great for you right now."
Seeing as the author is clearly quite knowledgeable about words and their meanings, the question is, then, why is she making such a flimsy case? The answer is, perhaps, to be found in the conclusion:
Please don’t take this the wrong way — and really, I hate to say it — but the true audience for the but-head may not be our listeners, but ourselves.