I think the idea is that there is an objective morality but any individual may be wrong about what it is. He's confident that an answer exists but not that he has found the right answer.
That's how I read it anyway.
Yes, though I'm a bit more confident at least on some issues, I know I could be mistaken.
I'll try using the slavery example a bit differently. Let's say at a particular time and place in history, 100% of the earth's population agreed it was okay to enslave your enemies, rape them, kill or enslave their children, etc. They wouldn't like it done to them or their own group, but considered it acceptable to do it to others.
To me, even if there were such unanimity, that would not make it morally acceptable. Ethically acceptable by societal codes, but not morally. I believe that there is an objective morality by which such behaviour is always wrong, even if literally everyone alive believes it is okay, and even if literally everyone believes it is morally acceptable, literally everyone is wrong. That's the subjective morality, not objective. Even if the slaves and people being raped and killed believed what was being done was moral, would not make it so, and even if they believed it was. Contrariwise, if one person believed slavery was wrong, and helped slaves escape, even if others thought it was wrong, even if they thought it was wrong, it would be objectively morally just (vis-a-vis Huck Finn, tormented that in helping Jim escape he is doing wrong...).
While I am religious and so see some moral absolutes in that light, I also think that in some cases, even proceeding from reason alone, it may be possible to arrive at objective moral truths on some topics, by logic, reason, Kantian ethics, whatever, and the golden rule may be one such, even if it's application in various circumstances is less certain. For instance, letting adult people do what they want even if dangerous to them, do we distinguish between suicide because of painful disease versus suicide because of treatable mental illness they don't want treated, or do we intervene to try to put them in a condition in which they can exercise their reason? What about drug addiction versus recreational non-addictive behaviour that carries the risk of addiction? Do we prohibit dangerous foods or drugs but allow dangerous sports, or prohibit the latter also? Protection of speech is one of the toughest.