Back in the day people would have just been honest that they thought this stuff came down from some kind of divine entity.

When you strip the religious aspect out, it just stops making sense. You're reduced to making vague arguments about "natural" law or tradition. They're talking about "enduring" values here, so I guess the angle is some kind of legal darwinism - the values have survived so far so they must be good and representative of what the people actually want. Because, as we all know, values get to just compete in the free marketplace of ideas and the best ones win out, there's never been a case of a political elite working to maintain the values that benefit them and crush the ones that don't.