I think that people might become health food freaks if they have something wrong with them in the first place. For example I have irritable bowel syndrome so I have to be careful what I eat because it makes it a little better although it doesn't make it go away completely.
If someone is sick because of the 'healthy' diet they follow, then it's likely they aren't getting enough of one of the food groups. I think something that can be easy to lack when following an extremely healthy diet (which very well might be a vegetarian/vegan) diet, is protein. As long as people are truly educated about nutrition and aware of their body's needs then following a healthy diet shouldn't make someone sick - quite the opposite, in fact.