I'm in the group 2 camp, because while I try to eat only until satisfied, and I do believe that portion sizes matter, I don't agree with the absolute supremacy of calorie math.

This is partly the result of my own personal experience, since I switched to Atkins after a year of strict low-calorie dieting. I lost 25 lbs during that year, eating 1200-1400 calories a day, and had stopped losing weight altogether and even put back a pound or two. When I switched to Atkins, I kept track of my calorie intake, but didn't really restrict it other than not overstuffing myself or snacking between meals. I've averaged pretty much between 1800-2100 calories the whole time I've been on Atkins, considerably higher than my previous low-cal intake, but I lost weight much, much faster -- 30 lbs in 3 months, at the beginning. I still eat about that many calories, even at my current weight, and am actually still losing very slowly. I exercise almost daily for 30 minutes of cardio or an hour of weights, but I'm not a marathon runner; my job (computer programming) is completely sedentary, and I work from home, so I don't even get the minimal exercise that walking around a large office building provides. Nor do I have some kind of magic hyperactive metabolism -- I've been overweight most of my life, managed to get up to 210 lbs, and lost relatively slowly on my previous diet. I'm also not massively insulin-resistant, as evidenced by the fact that I lost steadily and well at a relatively high carb level (35-50g).

The only explanation that makes sense is that there is something unique about Atkins that works particularly well for me and has allowed me to lose more weight than my caloric input/expenditure would predict. If you look at my initial loss, there's NO WAY to account for it with calorie math alone. 30 lbs in 3 months works out to a constant 1200-calorie deficit EVERY DAY for 90 days; I wasn't exercising at all at the time and had the same lifestyle activitity as now, so every bit of that loss came from my diet, and there are only a couple potential explanations. If my maintenance caloric level was 3000 calories a day (e.g. 1200 above my intake), I should have been losing even faster on low-cal (not to mention that that's a ridiculously high # maintenance level of calories for someone at my former weight). It's equally unlikely that I was just eating a lot less than I thought, at least enough less to explain that huge sustained deficit; I'm scientifically minded and pretty competent with a food scale, and would stake my life that I wasn't overestimating my calorie intake by more than 100 or so calories a day, not enough to explain that loss. I'm also pretty confident that the majority of that loss was fat, not muscle or water, because I also dropped a bunch of inches and went from a tight 16 to a loose 12. So yes, I'm skeptical when I see someone say it's primarily or exclusively about the calories, because I can't come up with any logical way to reconcile that with the facts of my experience. Clearly, there was some other factor at work, and Occam's razor says it's got to be the carbs, since that was the only thing I changed.

I agree with you that there's a lot of nonsense being spouted about ketosis and induction, and I'm not claiming that calories are completely irrelevant. I've been known to say the same thing about wishing Dr. Atkins had just skipped the "induction" bit, and I've never even tested myself for ketosis. In fact, I'll even go you one better and say that I wish DANDR focused more heavily on the glycemic index than on sticking to a magic carb level, because 20g of veggies is totally different from 20g of splenda and cream and cheese. However, I do think there's more importance to (low-GI) carbs than merely healing a damaged insulin mechanism, and that the calorie theory has some serious flaws in it. It's an insufficient explanation for people who are really successful with Atkins, and that implies that it's also an insufficient explanation for people who really struggle as well.