As far as cheese goes, it is not unlimited Dr. A suggest 3 to 4 oz per day at most. I don't believe that any of the foods are actually what I a person would call unlimited. Dr. Atkins said to eat when hungry and not until stuffed or full, only until satisfied. Also he says that even though we don't really count calories on this WOL/WOE that calories do count. So if you want to reach a goal weight of 165 your calorie intake should range from 1650 to 1980 a day, therefore if you ate unlimited amounts of food even with a low carb intake, you may still not see the loss you hope for.
These foods such as the ones on the induction list of acceptable foods should be eaten liberally, not unlimited.
Hope I was able to answer your question somewhat.