This is a reasonable statement of the Orthodox Christian position, and it can certainly be interpreted to mean that our human moral urges are the result of some kind of divine intervention, even if this involved God in some genetic engineering. But God is not a necessary player in these explanations; and a godless evolved morality would look just the same as the one we actually have. Here's why.
One of the distinctive things about moral feeling, as opposed to moral reasoning, is that it is not consequential. It is not the result of a process of conscious calculation: we calculate in order to check our intuitions, but the intuitions themselves seem given; when they differ from calculation, our first instinct is to re-check the calculus, and not the emotional compass. I am talking here about the sense that there is a moral compass, and that right and wrong do exist as absolutes outside ourselves, which is one of the things that classical Christian apologetics assumes is a human universal, and very likely it is. Just which acts qualify as right and noble, or wrong and ignoble, varies wildly from culture to culture; and some have different moral weights within cultures, depending on their context. But the tendency to classify actions as right and wrong, repulsive and admirable, do seem to be universal constituents of humanity and both Christians and evolutionary psychologists should be happy with this idea.
Sociobiologists are generally happier with the idea that it is simple aversions and desires that are genetically encoded. There is a difference; and it is important, as can be seen by the proposal that we have innate defences against incest. Incest has fairly deleterious consequences for populations that do a lot of it, so you would expect such defences to evolve. The most popular theory is that in humans as (we suppose) in other animals the defence is not a moral appeal. We just don't find sexually attractive as adults people with whom we were, so to say, litter- mates in infancy. This mechanism would not operate between parents and children, which explains Lot and his daughters.
This is freedom from temptation, though, which is not what people mean by a moral sense. That would involve firstly being able to recognise something as a temptation; and secondly being able to resist it. Could such a more complex set of feelings have evolved? I think the answer is quite clearly "yes"; and that our intuitions about the existence of an absolute morality are a way of dramatising the conflicts that result.
The whole point about feelings or instincts in an evolutionary analysis is that they can also be analysed as strategies. You can look at the behaviour of an animal, or a human from the outside and see how it is likely to spread through a population at the expense of other behaviours; but when you look at it from the inside, you do not make these calculations: you are part of them. Nobody thinks "It would make sense to behave towards this lion as if I were frightened of it and run away". They think with their feet and by the time the thought has emerged into something as coherent as "aaaaaargh!" they have, if well-adapted, already run 20 yards.
The strategy which the emotions encode can only be reconstructed in tranquillity. And if it is true that we have moral instincts, then they too will be like this. They will in some sense encode a strategy which has proved more useful in the past than its alternatives but we won't learn from them what it is. The strategic usefulness of emotions is obvious with those so primitive and so widely shared across the animal kingdom that we think of them as completely natural: we panic if short of breath; we grow very distressed if short of food.
Other more specifically human emotional habits such as depression or some of the ways in which we experience pain are harder to explain as strategies; but it is possible, if they are carefully analysed, to come up with perfectly respectable accounts of why they might make sense in most contexts. But these analyses always come long after the fact. A man paralysed by pain does not think "I am maximising my chances of worsening an infected stomach wound". He just knows he must not move.
In a similar way, we would expect our moral impulses to come sometimes with completely unanswerable force. It seems to be a distinguishing mark of religious experience or transformation that it is unanswerable and largely incommunicable. You just know, overwhelmingly, that the world is a fundamentally good place, or that some evil must be resisted. It is a way of making decisions at once and forever. In this it does not differ importantly from other evolved emotions. There's no need for God to have twiddled our genes to get there.
But the argument has one last twist: evolved emotions don't survive unless they encode strategies that work and unless the insights that they give us are in some sense true.