If propagation is replicative, as it is in biology, then stability arises from the fidelity of that replication, and hence an explanation of stability comes from an explanation of how and why this high-fidelity is achieved. If, on the other hand, propagation is reconstructive (as it is in culture), then stability arises from the fact that a subclass of cultural types are easily re-producible, while others are not, and hence an explanation of stability comes from a description of what types are easily re-producible, and an explanation of why they are.The problem I see with this is that 'reconstruction' is not confined to cultural evolution, it happens in the organic realm as well. Stability of DNA-based creatures is not explained simply by invoking high-fidelity copying. Living fossils illustrate stability comes from other sources. Nobody in their right mind would argue that Alligators or Ginkgo Biloba trees resemble their ancestors from millions of years ago only because of high fidelity copying. That would be failing to give longevity and fecundity their due. It's not that mutations affecting leaf shapes and leg lengths never arise due to high copying fidelity. Rather these stable forms represent adaptive peaks: sweet spots in the fitness landscape that are hard to improve on. In dynamical systems theory such spots are sometimes known as 'attractors' in state space.
In both organic and cultural evolution, stability is explained by a mixture of high copying fidelity, longevity and fecundity. Characterizing stability in organic evolution as only the result of copying fidelity is a mistake. In both organic and cultural realms, some entities are also better at reproducing themselves than other ones, and are more long-lived than other ones. The fitness landscapes they evolve on have stable adaptive peaks that result in stable forms that can last for hundreds of millions of years. We can use much the same theory of adaptive peaks and adaptive stability in both organic and cultural evolution.
I think the reason confusion over this issue arises is due to a misclassification of generation times. If you look at one generation, then it might seem that fidelity is the only factor in the organic realm - since longevity and fecundity take time to measure. While in one generation of cultural evolution, all kinds of reconstructions can happen - inside a mind. The problem here is that extra generations have been ignored in the cultural case. There's all kinds of copying with variation and selection going on within the mind, representing generations which are simply not being counted. Comparing one generation in the organic realm with multiple generations (within a single mind) in the cultural case is where the comparison comes unstuck.
Stability from sources other than copying fidelity - and adaptive peaks (A.K.A. attractors) - are well known and well understood in conventional evolutionary theory. However, not all anthropologists appear to be aware of this. They apparently think that these are newfangled discoveries associated with cultural evolution.