My SIL recently did a naturopathic oral 'hcg diet' that had an induction period at 500cal/day. It also included NO grains, NO fats/oils except coconut oil, NO processed foods. It DID include bacon, meat and lots of veggies and a tiny bit of fruit. Fats, fruits, nuts, dairy etc were added back in gradually.
SIL swears it was the hcg that got her through the 'carb flu' and made the weight fall off. The 500cal/day had nothing to do with it

I asked her if she knew she was on a Paleo diet. She said, yes I heard its something like that...
On a positive note, she is convinced her sugar addiction has been cured. AND she is reading Wheat Belly. And this is the longest I've seen her stick to any one beneficial way of eating. Now if only I can convince her to stop buying all their CAFO meat at Costco.