Wow! Just when you think Atkins was a bad method. I just stumbled across the Stillman's diet (or 'no veggies' or added fat diet). Yep, You eat only meat, dairy & eggs. No added veggies or fruits & no added oil - Now that's madness! So, constipation & nutrient deficiency is going to be an issue pretty quickly I'd say - what a crazy idea.
Couple of links:
Wiki
Trivia library