Sorry to push in again, but Bradski really is right in a sense. Unless the issue is specifically moral theology, then simply invoking God isn’t going to help anything, because we don’t have access to the divine intellect any more than we have access to creatures. Natural reason does not apprehend God directly. Thus, we find out morality, if at all, through nature. Traditionally, the Catholic intellectual tradition has understood this to be natural law and virtue ethics, which is simply the full development of realizing that nature is teleological. Now, it is surely granted that such teleology is eventually grounded in the divine intellect (a la Leah Libresco), but again, we only have access to that to begin with inasmuch as we know God through creatures. We don’t appeal to the divine intellect to get answers to moral dilemmas. We appeal to morality to get answers to moral dilemmas; and only appeal to the divine intellect in these situations to get answers as to where and how morality is grounded.
Pushing the same point, it’s not merely that we know morality through natural law, but it is in fact natural law that determines morality. Teleology functions differently in reference to different natures. If God created different natures, you have different teleology, and therefore different natural law/virtue ethics. (Of course there are going to be constants no matter how much things are changed up, since we would always be dealing with rational creatures.) While “should” and “ought” are grounded eventually in God because teleology is grounded in God, moral obligations and permissions, but especially virtue, are grounded in natural law, and so they do not require any immediate recourse to God; for it is precisely natural law that God uses to determine morality for creatures. We might say that natural law is the moral lawgiver, even if God is the giver of natural law. An atheist could say with certainty that natural law determines contraception to be a seriously immoral act. There’s no contradiction, because there’s no proximate reference to God. Would he be inconsistent on account of teleology itself? Sure, we could grant that, but that’s another matter altogether. The point is that invoking God in rational discourse does not resolve moral dilemmas; it resolves being inconsistent about what you think is the grounding point for objective morality. But it is the objective morality itself that resolves moral dilemmas.
Of course, an atheist might not appeal to natural law at all, but if he appeals to a valid moral point demonstrated by reason, he would effectively be appealing to natural law under a different name and application. What else is there?