Well I draw this conclusion based on what I know and suspect. Take psoriasis, an autoimmune disease, which I know oh-too-well. ;) There are genetic markers associated with this disease but it is felt environmental factors have a heavy influence in determining whether one would actually develop it. If genetics were entirely the cause for the disease then identical twins would either both have the disease or none of them would. In fact I believe there is a 60% chance of both twins getting this disease if one gets it. So obviously environmental factors are involved. One can change one's environment but changing one's genetics is not so easy.
Now I assume in the case of the type of Breast Cancer Ms. Jolie was facing is very heavily influenced by genetic factors. When doctors say she has an 87% chance of getting the disease it sounds like this is based on sound data. Could Iodine supplementation or some other alternative treatment lessen this 87% value? I don't know, I am not a Breast Cancer expert. I suspect there are several different categories of breast cancers sufferers. Probably only a subset of Breast Cancer sufferers share the same genetic markers as Ms. Jolie. Others don't. It would be interesting to understand about which forms of breast cancer are mostly sparked by environmental factors. And most certainly, Iodine deficiency can be an environmental factor.