Ah. The term "selfish gene" is not meant to reference an actual physical gene, it's only a description of the human dna being selfish as a whole. It's a basic belief of any darwinist.
If morality comes naturally to us, the question is why? Is it because of some directed action from God, or is it because of directed action of selfish genetics? (e.g. morality ensures the survival of the community, and the community ensures the survival of the individuals, and thus as a long term protective strategy, it is a direct expression of the selfish gene). If however, the selfish gene is non-existent, and the genetic code is merely a physical blueprint, then the hand of God must be involved to propagate the species via the creation of things such as culture, society, morality, etc. To that effect, what you call natural morality is nothing more than the memes of morality from a religious society at large infecting the so-called non-religious. Spooky...
So besides Richard Dawkins, have you read Snowcrash?
Another school of thought simply states that God is just as likely to be directing the action from below as he is from above, as he is the God of all small things as well; things as small as DNA say.
Calvin