Have to say that I'm curious too. I simulated it in LT Spice really quick and couldn't see a difference (for a pure sine wave at least). If I could hazard a guess... it would be something to do with blocking either DC components to the wave (really unlikely), or high freq responses. If I have some time, I might simulate it some more, but that might be what you can look into.
As a side note, I've looked at a lot of linear supply designs and I can't say I've ever seen caps across the diodes. Not that that means anything.