I think that rather depends on what your definition of "healthy" and "balanced" are. The second link that you provided refers to Atkins as "wildly unbalanced", but doesn't really state why they consider it so.
The nutritional needs of a growing 15 year old attempting a serious body building regime are quite different from that of a post menopausal woman who exercises moderately.
Besides...what's wildly unbalanced about adequate protein, healthy fats, a large variety of vegetables and small amounts of low glycemic fruits?