Blanket statements like the ones quoted from the site are never good... but switching from a moderate fat and protein and very high green veggie diet to a diet primarily of raw meat, raw eggs, raw fat and butter has completely changed my life. I feel so good..I won't even get into the long list of sympoms which have diminished or disappeared. Before eating this way I very much believed in a 65-80% veggie and the rest protein way of eating.
Perhaps part of what CAN make a person feel worse on low carb is their food choices. There are a lot of over processed and over cooked foods that people can lose weight on, yet not feel great. I think overcooked meat, cheese, and other crap items are what will contribute to the constipation that a raw fatty/meaty diet would not encourage.
Every one has to figure out what makes them feel best.
However, I'll second the fact that grains can be associated with many degenerative, inflammatory and autoimmune conditions, AND that too much omega 6 is bad.
As for this diet being the opposite of all cancer cure diets - check out Aajonus Vonderplanitz (yea, weird name). He has an astonishing success rate with his clients in terms of "curing" incurable diseases and cancers, as well as his own. He's been eating this way for 33 years (raw meat, raw milk, raw fat, raw honey, raw eggs, few veggies) and according to every reference is in a very healthful and robust condition.
There are many carcinogens associated with cooked and esp. over cooked food. Maybe the answer lies less in how many carbs one eats but how fresh and natural their food is? Also, don't forget that a person's genetic constitution has a lot to do with how much their body can take. Unfortunately for some it does not take much abuse to make them sickly and weak, others can eat pizza, drink coke and smoke for their entire lives and not feel poorly.
www.mercola.com/2001/jan/21/weston_price.htm
www.angelfire.com/ny2/bass/disease-cure.html
..just for kicks...
www.karlloren.com/aajonus/index.htm