I always thought that the shunt diodes were needed The conceptual model that one diode is on during each half cycle shorting out the corresponding cap isnt quite right  What really happens is that the node between the two caps gets charged up or down depending on whether the  or  ends are connected together and stays charged so that both caps are biased with sufficient dc that their voltage never goes negative  The reliable source we have cited there app note from a cap manufacturer says that you dont really need the diodes because the caps will act as diodes and conduct in the reverse direction to accomplish that effect  I would think it would be more reliable to have that reversed current flow through a diode but given that its only a transient phenomenon as the cap charges up I can see that in some applications it could be acceptable to do it without the diodes