I have both the 1992 and 2002 versions of his book. in the 1992 version he specifically says that the Atkins diet is not actually a high fat diet.. The purpose of fat in the diet is two fold. I,) Fat satiates the appetite. 2.) Fat makes otherwise bland diet food taste better.
Fat will not hurt you on the Atkins diet, but people often seem to think of it as a high fat diet rather than a low carbohydrate diet. Atkins also says that people with a real aversion to fat can do a low fat version using leaner cuts of meat or even a vegetarian version though their menu choices would be extremely limited.
In a practical sense, if you severly limit the carbs, there is not a lot left other then fat and protein