I want to add that I spent 1 or 2 hours reading over this awesome tutorial:
http://www.analog.com/static/imported-files/tutorials/450968421DDS_Tutorial_rev12-2-99.pdf
It has kind of answered what was happening, but I still don't understand why it is happening.
I can only think that it has to do with the step-like output of the DAC but getting from this to repeating images and inverses of the original signal still blows my mind.