Galactor

in other words people are endowed with the natural ability to arrive at the truth through their use of reason,

Indeed. They have been "endowed" just as other creatures have been endowed with a moral sense by the slow process of evolution. This is not only well understood and researched, it is by a country mile, the best explanation we have for morality. It fits.

The simplest and best explanation is that moral truths don't exist.

It makes no sense to talk about "arriving at the truth" or a "moral sense" unless morality is something objectively real and moral statements are statements about that reality. The fact that humans have evolved to believe that certain behaviours are "good" and others are "wrong" doesn't mean that morality has a real existence any more than the fact that we may have evolved a tendency towards belief in the supernatural implies that there is a God. Moral beliefs are not morality, any more than religion is God, yet people often talk as if they are the same thing. If moral beliefs, customs and norms are morality itself, how could there be such a thing as a false moral belief? That would be like saying there is a false fashion or a false musical genre.