The trouble is that the AMA opposition is based more on its own prejudices than on science. So far, the medical establishment has refused to even test whether the diet works. Meanwhile, a lot of people report that the diet works, while other diets don't.
Update: Monday's CNN Crossfire had a debate on this. The right-winger took the side of eating fatty foods and following empirical scientific evidence. The left-winger took the side of telling people to eat what nutritionists think people ought to be eating. I think that the right-winger got the best of the argument.