From what I can tell, that presentation is assuming a certain class of graph structures in its DACB example - for example that there isn't an element E that can

From what I can tell, that presentation is assuming a certain class of graph structures in its DACB example - for example that there isn't an element E that can causally link the other nodes, emulating a causal relationship without there being one. Assuming a class of structures is not a general approach; in my example this would be the equivalent of assuming there is no sprinkler, but how can you make that assumption from the data alone? There's another issue: their approach is statistical, so even if you assume a class of graph structures you can only draw conclusions that the causal structure "almost surely" exists, not that it does exist. What this means is that even within infinite data, you can't prove that the other structures are impossible. If I turn on my sprinkler when it rains the first {very large number} times, you may conclude that there is almost surely a causal link between the rain and wet grass, but there is no reason I have to do it. You aren't left with a proof.