@imnotarobot are you saying that an alternative solution is to set the Name and Password option? It seems that the only solution provided is to set the 'root' password (actually, "Change Root Password" in the Directory Utility Edit menu).
Question for everyone: If the problem is that root is available with a blank password, why not just choose "Disable Root User" in the Directory Utility Edit menu? At least for non-power users, or those power users who don't mind utilizing sudo? Or is that not a viable alternative solution?