You're confused, I guess.

Rights aren't natural things.

Absolute morality would be a natural thing, if it existed. Morality is a social construct. If we believe that the objective of morality is to promote the well-being of (populations and) individuals, then there may well be cases where it is perceived to be moral to do horrendous things. "Thou shalt not kill" is clearly an immoral (harmful) restriction in certain cases. Whether one chooses to call the vast majority of killings "immoral" or "absolutely immoral" is simply semantics.

Just to be clear, a dictator can impose universal human rights. Not everyone is required to agree that it's a good idea for that dictator to do so.

Also, I do believe that killing someone for adultery is/was always wrong, but not that it's necessarily absurd for ordinary people to believe in the value or decency of such an act.

"Do you think adultery ought to be punishable by death?". Why is it that a majority in Spain would say "no", while a majority of a certain tribe in Brazil, or a majority in some desert country might say "yes"? You cannot arrive at a somewhat serious answer without really exploring the value, both perceived and quantifiable, of things like monogamy to partners, their children, the family and society at large... Morality is an, at times impossible, balancing act centered around emotion, personal experience/ignorance, shared wisdom/idiocy, empathy and intelligence. Not only that, but a moral judgment always takes place in a social reality, which appears very real and natural. In certain settings doing the most moral thing requires you to become a moral deviant. In a society which rejects moral absolutes, while still recognizing the importance of shared ideas centered around wellbeing, individuals don't need to adopt the psychology of moral deviants/prophets to get to a place where reason trumps custom. It also allows for ideas to be rationally discussed. It's not hard to imagine the benefits...

Basically Dawkins is spot-on. He didn't talk about the core beliefs one can adopt to guarantee that one will always think and/or act morally. It just doesn't work that way. We weren't designed, let alone designed with a "good switch" or a "truth switch".