What the SEP actually says is, "Moral realists are those who think that, in these respects, things should be taken at face value—moral claims do purport to report facts and are true if they get the facts right," and that's it.
This is all a matter of misunderstanding the meaning of words, and nobody is objectively right or wrong about that, since the disagreement is widespread - I'm not the only one to complain.
To me, an unqualified "fact" is, by implication, a simple claim about the universe, not a fact about the person holding the belief in that fact. An unqualified "fact" should be true or false in itself, without requiring you to further specify you meant the instance-of-that-fact that applies to some particular person with particular moral beliefs.
If SEP's usage of "fact" is taken to mean "a fact about the person holding the moral belief", the fact being that the person does hold that belief, then I don't understand what it would mean to say that there aren't any moral facts (i.e. moral anti-realism). Would it mean to claim that people have no moral beliefs? That's obviously false.
On Eliezer's view, as I understand it, human!morality just is morality, simpliciter.
That's exactly what bothers me - that he (and other people agree with this) redefines the word "morality" to mean human!morality, and this confuses people (I'm not the only one) who expect that word to mean something else, depending on context. (For example, the meta-concept of morality, as opposed to a concrete set of moral beliefs such as Eliezer!morality or humanity!morality.)
I agree that if everyone agreed to Eliezer's usage, then discussing morality would be easier. But it's just a fact that many people use the word differently from him. And when faced with such inconsistency, I would prefer that people either always qualify their usage, or taboo the word entirely.
I think the problem lies in your usage of the phrase "objective fact".
For example, if I claim "broccoli is tasty", my claim purports to report a fact. Plausibly, it purports to report a fact about me -- namely, that I like broccoli. If someone else were to claim "broccoli is tasty", her utterance would also purport to report a fact -- plausibly, the fact that she likes broccoli. So two token utterances of the very same type may pick out different facts. If this is the case, "broccoli is tasty" is true when assert...
Continuing my quest to untangle people's confusions about Eliezer's metaethics... I've started to wonder if maybe some people have the intuition that the orthogonality thesis is at odds with moral realism.
I personally have a very hard time seeing why anyone would think that, perhaps in part because of my experience in philosophy of religion. Theistic apologists would love to be able to say, "moral realism, therefore a sufficiently intelligent being would also be good." It would help patch some obvious holes in their arguments and help them respond to things like Stephen Law's Evil God Challenge. But they mostly don't even try to argue that, for whatever reason.
You did see philosophers claiming things like that back in the bad old days before Kant, which raises the question of what's changed. I suspect the reason is fairly mundane, though: before Kant (roughly), it was not only dangerous to be an atheist, it was dangerous to question that the existence of God could be proven through reason (because it would get you suspected of being an atheist). It was even dangerous to advocated philosophical views that might possibly undermine the standard arguments for the existence of God. That guaranteed that philosophers could used whatever half-baked premises they wanted in constructing arguments for the existence of God, and have little fear of being contradicted.
Besides, even if you think an all-knowing would also necessarily be perfectly good, it still seems perfectly possible to have an otherwise all-knowing being with a horrible blind spot regarding morality.
On the other hand, in the comments of a post on the orthogonality thesis, Stuart Armstrong mentions that:
This is not super-enlightening, partly because Stuart is talking about people whose views he admits he doesn't understand... but on the other hand, maybe Stuart agrees that there is some kind of conflict there, since he seems to imply that he himself rejects moral realism.
I realize I'm struggling a bit to guess what people could be thinking here, but I suspect some people are thinking it, so... anyone?