I'm really not against specific diets (within reason of course) that can be used to drop weight fast. I'm not even against very low calorie diets or even fasting. But I'd consider those tools and use them as such - use them temporarily, make sure you know what the implications are, and what you will do once they are over.
My issue with some diets or programs is that they usually make statements that are not true and never really teach you anything about weight loss, so you can never work outside of the 'system' those programs were built on.
From that link, statements number 1, 4 and 5 are point-less statements. You can not know or notice if you have less toxins on your body, or if you are more efficient creating energy.
Numbers 3, 6 and 7 can be said by most diets that are sensible. Most diet programs are better than the average diet and most (sensible) diets will result in improved health compared to the standard diet of an overweight person.
Number 2 is my main problem. They'll will blame toxins for weight gain, and tell you to cut them out. And then they'll give you a list of foods high in toxins. But most likely those foods will be high calorie foods that folks tend to overeat, and by cutting them out and replacing them with something else, you have instantly reduced the calories of what you ate - resulting on weight loss.
The point I'm trying to make is that while the program may work, they are of no use when the 'message' they give is false. Those don't work on the long term and leave folks with all sorts of wrong ideas.
Your sister IS running a caloric deficit by following that plan, because the foods in that plan are low in calories. But it isn't the 'detox' that is working, it is the lower calories.
It is perfectly possible to run a deficit without having to actually count the calories. One just needs to be smart about the food choices. That's why I mentioned things like volumetrics or making substitutions, those things can work, and without necessarily having to restrict anything.
Emphasizing on foods that are lower on calories (this is pretty much what volumetrics is all about), and being careful with calorie-dense foods can really help and it's actually a great way to run a deficit without having to directly count the calories.
There are really a lot of ways to do the same thing (running a calorie deficit). Some folks limit what they eat to a certain groups of food, or to a list of foods, some limit the amount of meals they eat a day, some folks do intermittent fasting and that helps them eat less, etc.
I should mention that you can do the same by also adding good habits too. Drink some water 15 min before eating, fill half of your plate with vegetables, make sure you get enough fiber, try to eat your calories instead of drinking them, if you're still hungry wait at least 20 min before eating again, have a non-caloric (don't add anything) drink with meals (tea, coffee). Those are all valid ways to help you lower the calories without having to count them. And all those are sustainable habits you can apply under most circumstances.
You can build your own plan based on a combination of those things and have success with it without having to go through different diets or eating plans.
