If you are right to believe that religious faith offers the only real basis for morality, then atheists should be less moral than believers. In fact, they should be utterly immoral.
Vallicella's criticism of it is exactly right. For my part, I was reminded (as I always am when this topic comes up) of William Warburton. Warburton was an eighteenth-century theologian and philosopher, extremely influential at the time, who was famous for being very abusive and unfair in his treatment of his opponents, including atheists. He has an extended argument, called The Divine Legation of Moses, a good portion of which is taken up with arguing precisely that religious faith offers the only real basis for morality. Warburton takes a very strong view of the matter: atheists cannot consistently recognize any moral obligation as an obligation, because obligation requires the sanction of a prior superior will, and atheists in general don't recognize any such will.
But, of course, Warburton doesn't think atheism is true, and he thinks God exerts a moral providence. So he denies that atheists are utterly immoral; divine providence has prevented all human beings from being utterly immoral by giving every human being (1) a moral taste, a set of natural sentiments and preferences, that can be cultivated and shaped; and (2) a reason capable of recognizing whether something is (as a matter of prudence) appropriate or inappropriate. Warburton considers neither of these to be morality in the proper sense, but they are (we might say) morality-tending, that is, by God's providence they approximate (to varying degrees) moral behavior, because even for theists they serve as the God-designed materials for moral life that are given proper form by divine command. Moreover, Warburton is only committed to saying that atheists cannot consistently be moral even in what he considers to be the only proper sense of 'moral'. For atheists do not all exist in Atheist Land. They exist in a world where they have to live with theists, and are exposed to theistic ideas, and are sometimes raised and educated as far as their moral life is concerned by theists. So it's entirely possible for the moral teaching of theists to have rubbed off on atheists, either directly (e.g., in their acceptance of some of the law of Moses or Jesus' Sermon on the Mount as good moral guidance) or indirectly (e.g., by shaping the general culture in which they live). Likewise, some atheists may follow the teaching more thoroughly than some theists, although Warburton thinks that in doing so atheists would be implicitly contradicting their atheism without really realizing that they were doing so (because exhibiting the contradiction would take extended reasoning about the nature of obligation).
Thus even Warburton, who definitely and vehemently holds the view that the only real basis for morality is religious belief, is not committed to the claim that atheists are "utterly immoral". He's only committed to the claim that when they are moral they are (fortunately for themselves and everyone else) rationally inconsistent or confused. And this tends to be generally the case for people who make this claim. As Vallicella notes, Harris is conflating two distinct questions.