"I cannot even imagine being in such a bizarre situation that an atheist would be asked to deliver an invocation. An atheist giving an "invocation" sounds like mental masturbation to me."
Not so bizarre. I've been an active member on many boards of directors and an officer of several organizations. All normally began their meetings with some sort of invocation. As a member, I've often come up in the rotation for delivering such a thing.
While most invocations ask some deity to protect the group and guide its decisions, mine were somewhat different. I always simply ask the group to carefully consider the issues that will be discussed and make their best decision, based on their assessment of the issues. I appeal to logic and intellect.
I never denigrate anyone's faith, and never would. I do not share any religious faith with them, but I do share a common concern for fairness and proper actions.
Not once, in all the times I've done this, has anyone objected to my words. It is not so bizarre.