I agree - when I was ill I would not eat any fat or oils. As I became more health aware I realised I needed them, and started to take fish oil capsules at first, then gradually started eating other types of oils/fats.
Essential fatty acids actually help to kick start the bodies fat burning mechanism, and I found that I didn't put on any weight, but it became much easier to eat normally, and not be prone to binges.
I am sure that if I hadn't have done this when I did, I would be a wreck by now.