I have been involved in several discussions of late regarding calories and do they matter or not. I know that many people that are on a Low-Carb diet have somehow come to the conclusion that they do not. In Dr. Atkins book he suggest in the beginning that your primary concern should be carbs and to eat when hungry and stop when full.
My best guess is that people either read this excerpt and determined from it that calories don't matter or they heard it somewhere and took it as fact. For those of you have read DANDR (Dr. Atkins New Diet Revolution) he was very specific that calories matter.
You body needs a certain amount of calories per day based on your personal rate of metabolism. This is known as your Base Metabolic Rate (BMR) and can vary greatly in 2 people with the exact physical makeup based on activity levels, genetics, etc. This part I think we all understand, however.
Physics First Law of Thermodynamics:
"Energy can neither be created or destroyed, it can only change forms."
If I am a person that needs 2000 calories to get through a typical day. Then any surplus I consume will be stored (change form) for future use. However, if you have a deficit by say taking in 1600 calories. Your body will need 400 calories from somewhere. It will then use your fat stores to convert this stored energy (change form).
Atkins works not because you are in Ketosis and you can consume whatever you want and still lose weight. It works because the lack of carbohydrates in your diet helps control instability in your blood glucose which will ultimately lead to hunger and more instability. The cycle will repeat itself and you will eventually take in way to many calories and always be working with a surplus of calories. Since they cannot be destroyed they will be converted to a different form. FAT.
Because you have already converted your body to utilizing it's own built-in anti-starvation mechanism having a deficit of calories in a given day will mean your body will not pause and figure out how to make up the deficit. Ketones are in place and your body goes to work making ketones to burn for energy.
It's really as simple as that. Calories in calories out is not an exact science since we are all somewhat unique physiologically. However, the differences for a typical person are not so great that the laws of thermodynamics don't apply.