I do know exactly what you mean about the starvation theory thing but what you have to remember is that people who are anorexic weren't fat and then just stopped eating. They were probably a healthy weight or possibly even a little overweight and then have started dieting like you and me and the rest of us. They have then lost weight but then not known when to stop and taken it to an extreme. They have already lost most of their fat through ordinary dieting before ending up doing the starvation thing due to anorexia. You must also remember that their starvation has been a long term thing - they've not become so very thin in a fortnight. They've not eaten properly for years often.
Circes is right, when the body has no fuel and nourishment it will start to devour itself. Muscle and organs will be used in order to survive. That's why anorexics are literally skin and bone - their body has used up the muscle too.
Not wishing to diss any particular diet plan because different things work for different people, I agree with you that, in principle, losing weight is a straightforward equation 'Eat less + exercise more = lose weight'.
Putting exercise aside for the minute, let's say your body needs 1,800 calories a day (your basal metabolic rate) just to cover the basics of survival and everyday activities. You reduce that to 1000 calories a day and your body still needs to get 800 from somewhere (fat!) You need to get rid of 3,500 calories in order to lose 1lb of fat. So, for arguments sake, when you're 'losing' 800 calories a day, in just over four days you should be managing to lose one pound.
Now factor in the exercise. You mention doing more walking. Are you walking at pace or are you ambling along? How long are you walking for? Yes, even if you amble along for half an hour you will burn some calories, but you'll burn a hell of a lot more if you walk quickly and for a decent length of time. I don't buy into this 'do half an hour of exercise a day, broken down into 10 minute chunks if that's all you can manage'. I personally think that's bullshit. To really get some calories burned and make a difference to your fitness you need to exercise until you start to sweat and feel at least warm. What I'm basically saying is that if you are doing half an hour of easy walking then you might only be burning 70 calories whereas a really fast power work will maybe burn 200 calories in the same amount of time.
If you're doing the eat less/move more you do really need to move more!
Hope this makes sense. Sorry for rambling!!