I think during the episode we were too busy trying to understand After Virtue to just say straight out that the attempt to ground morality solely on cultural narratives just doesn't work, at least not to any more determinate degree than some of the other moral theories that MacIntyre suggests. In the Kant episode, I suggested that we need to use the principle of charity to apply the categorical imperative intelligently. One might well use Aristotle's term phrónēsis (practical wisdom) instead. In short, no rule can determine its own applications; we need smart people to do that, and in tough ethical dilemmas, wise people won't always make the same call. MacIntyre saw that underdetermination of actions by rules and declared that people will abuse that to then make the rules justify whatever they wanted to do anyway, i.e. as emotivists. In the episode, we really couldn't see how his own system got around this problem such that "the right thing to do" would be objective, even for one person embedded in a particular culture and circumstance, such that everyone with the relevant competence would judge the same way. The nagging threat of existentialism remains, i.e. that all such choices involve a creative act and not just astute obedience to an objective prescription.
By 2001, in his book Dependent Rational Animals: Why Human Beings Need the Virtues, MacIntyre had concluded that reference to biology, and not just culture, was necessary to make the project work. From the preface:
In After Virtue I had attempted to give an account of the place of the virtues, understood as Aristotle had understood them, within social practices, the lives of individuals and the lives of communities, while making that account independent of what I called Aristotle’s “metaphysical biology.” Although there is indeed good reason to repudiate important elements in Aristotle’s biology, I now judge that I was in error in supposing an ethics independent of biology to be possible…
Specifically, he argues that we are animals, and that our rationality makes us not so different than other animals, to whom he attributes beliefs, purposeful action, and social needs much like ours. He thinks that telos will come out an analysis of human dependency, in childhood and elsewhere. Though our rationality does give us a distinctively human nature (a "second nature") beyond our animal nature, there are important continuities between the two that helps us better understand human need: we don't just become autonomous moral agents, but need to be nurtured toward that, where much of that nurturing has nothing distinctly to do with our rationality. This doesn't so much replace the account in After Virtue as supplement it. He still emphasizes a key foundation for morality is the need for us to make ourselves intelligible to each other, so it's not just a matter of personal integrity (i.e. having a coherent sense of self), but being able to present this socially. We start life in debt: to our parents, to our culture, to each other. To participate in the kinships that we're born into (from p. 108):
I have to understand that what I am called upon to give may be quite disproportionate to what I have received and that those to whom I am called upon to give may well be those from whom I shall receive nothing. And I also have to understand that the care that I give to others has to be in an important way unconditional. Since the measure of what is required of me is determined in key part, even if not only, by their needs.
So the obligation is still mostly cultural, but MacIntyre is filling in the gaps re. being born into a culture. We're not just Lockean blank slates born into a culture and loaded up with baggage, but animals chock full of instincts and teleology, and that's going to fundamentally determine what culture is in the first place and how we relate to ours.
Note that I've not read this later MacIntyre work and can't attest to its quality or coherence. For more information on the progression of his thought through 2002, you can take a look at this paper by Kyla Scarborough that I found online, which provided the MacIntyre quotes above and most of what understanding I have of his 2001 book.