Help me understand XOR gate with diode logic
I have no problem spending a few bucks to build something and letting
  the magic smoke out of some components and finding out it won't work.
  What I do have a problem with is the fact that I just do not see how
  this works?


This will not work the way it is drawn, on both sides of the rectifier the voltage is positive. There is no way for current transfer to happen in this type of situation.

In circuit version B adding the resistors does nothing for the voltage on the terminals.

To understand and draw correct diagrams with rectifiers it helps to draw the two modes that the current can follow:

Source: Electronics and Communications

A rectifier could function like a xor function, but you have to keep track of all four situations. Lets say the rectifier has terminals A and B and the output would be the difference between the + and - terminals. So yes you are correct, it does function like a xor gate (except you'll have the diode voltage drop included)

Rectifier:
1) A- 0V B- 0V Output- 0V
2) A- 0V B-12V Output-12V
3) A-12V B- 0V Output-12V
4) A-12V B-12V Output- 0V