Probably so, but the fact of the matter is that it did not require her to be a Christian in order to understand the nature of marriage.
I think that is what one gets when one reads a little bit of context into the extract:
It is not because of her religious faith that Davis understands the nature of marriage. Non-Christians, too, have always understood (until the mania of the past few years) that marriage is a union of man and woman. That understanding was firmly in place long before the time of Christ.
But it was her Christian faith that was her reason for refusing to issue the marriage licenses. I would say that without that faith few if any people in her position would take the stance she took.