Bunny Mellon personally gave $700,000 to Edwards and filed for and paid a gift tax:
http://www.tax26.com/posts/external/4995/
That leaves a little over $200k in question, which Edwards also said was a gift from his now deceased campaign finance chairman.
Since the deceased cannot testify, and about 77% of questionable funds were indeed a gift, I do not know what the case is.
The man has done some horribly shitty stuff in his personal life that would make me question his ability to serve as President, but I don't think they have a case here.