I would question your point, "that moral values [...] are very strongly correlated [...] across societies". My favourite example is the Aztecs society. Moral values were completly different.

Sparta is another example. The Nazi regime in Germany too. Slavery in the US. I could keep going for another hour.

Moral values are highly dependent on you environmental influences.

Nevertheless you are totaly correct, that the majority of people in a single society shares similair views on moral rules.