Shermer is not a "skeptic" in the classical philosophical sense. This is a case where the old definition of the word and the new one are probably at odds. Clearly, he is a firm defender of science and empiricism, so he's all about withholding judgement until evidence is presented. (Also, notice how he challenges the idea that moral standards are timeless, so it seems like Shermer is already a proto- Epicurean, and in some points he comes off more Epicurean than she is. I wonder to what extent these types of podcasts may help many people realize that they already agree with most of Epicureanism).
Concerning your seventh point, she must be referring of the definition of justice as a covenant to "not harm or be harmed", which to be fair, is our version of the golden rule.
It seems like Wilson's views are tied to the belief that humanity has become progressively more compassionate and enlightened about many issues, and that we KNOW BETTER than the ancients in many regards. In other words, societies (like individuals) have the power to learn and engage in processes of moral development. We know that Epicurus dedicated a sermon to moral development, and we also know that Philodemus in "On Parrhesia" said that frank criticism is of two kinds: to an individual and to the society at large--so that the idea of moral development at the level of community exists.
This view has some merit, and deserves further consideration and discussion. It is one thing to say "ethics is eternal", which is not a clear statement, but it's another thing to say "we know better", with the implication being that some societies are more enlightened and therefore have conventions that generate more pleasure / less suffering to people than others, which is an undeniable fact. And if this is so, then what does this conception of moral development entail? I have a feeling that we may get closer to an answer to this by considering issues of mutual advantage in specific, concrete examples.