Perhaps “moral obligation” has a specific legalistic/Christian etymology.
This is one of the positions G.E.M. Anscombe defends in her influential essay “Modern Moral Philosophy”. She argues in part that the moral “ought” is a vestige of religious ethics, which doesn’t make much sense without a (divine) lawgiver. Indeed, one of the starting points of many modern virtue theorists is arguing that the specific moral sense of “ought” and moral sense of “good” are spurious and unfounded. One such view is in Philippa Foot’s Natural Goodness, which argues instead that the goodness ethics cares about is natural goodness and defect (e.g., “the wolf who fails to contribute to the hunt is defective” is supposed to be a statement about a natural, rather than moral, defect of the wolf).
I think DC’s point is that the donation one can makes from the proceeds of selling the kidney outweighs the counterfactual direct impact of donating the kidney.