That paper you linked is more of a different way of handling the parallax mapping itself but does not go into any detail on silhouettes that I could see. Most likely this is relying on the curvature thing since the tree roots are a perfect case for that. Basically if you know the current plane is going to bend by a certain amount, you can calculate when the ray would have exited the heightmap, or maybe the point at which the ray starts moving up in local space again and then you just kill it and return 0 alpha or something.