True, however, @Winston_Ewert penalizes more complex models. We can debate whether he did that correctly or not, but this objection is not really valid without a careful review of his penalization. I think a better question concerns the fit we would get from an undirected graph model versus a dependency graph (which is a directed graph), using the same penalization.
That is an important control to do. If it comes out wrong, it would undermine his argument significantly if the dependency graph model does not do better than the undirected graph. That, it seems, would be a speed bump for his proposal. As a matter of fact, we already know that human diversity data better fits an undirected graph than a tree. So the real question is if the dependency graph does better than an undirected graph, not just better than a tree.
It might be resolvable even if it initially fails this control. Perhaps the penalization function would need to be improved. It is, nonetheless, an important control study to run.
(side question to @Winston_Ewert, do the numbers in Table 4 include the penalization factor too?)