I'm not certain that this term applies to Karr, but on one of the crime shows the other night, a person was diagnosed with "factitious syndrome" and was similarly taking blame for something he hadn't done.
It's similar to Munchausen's and often relates to people faking an illness, but extends to people who lie to make themselves either victims or heroes in grand schemes.
The depth of detail is what distinguishes them from regular bald-face liars and the extreme attention-getting "reward" they try to achieve causes them to go to any lengths to convince others they're telling the truth.
What strikes me the most about the whole Karr episode is the fact that the Boulder DA actually took that professor seriously. He had already fingered several men as the killer before ratting out Karr.
I think that professor is also quite strange. He seems equally obsessed with the Ramsey case as is Karr, only in a different way. Karr seems to have some sense of guilt for her murder, and desperately wants to convince others of it. The prof seems to want to be the big hero who solves the case.
Speaking of which, this is a case that will likely never be solved. Everything we in the public know of the case suggests the child was killed either by a family member or someone very close to the family, not an stranger.