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 isn't 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 don't 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 it's 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.