I think that it's worth remembering the differences between epidemiology (which is basically data mining) and real experimental science.
Epidemiology is a strictly observational method for trying to spot relationships between certain variables in a large (and often dirty) dataset. Like all purely observational methodologies it cannot determine cause and effect. In this case they have found a statistical relationship between the amount of fat women ate in the EPIC study, and their propensity for breast cancer.
This is not the same as saying "fat causes an increased risk of breast cancer" because there might be some other confounding variable that influences both. To a certain extent you can use more statistics to try and eliminate possible confounding effects, but you can never be sure that you've eliminated them all. There are other problems with epidemiology too, a big one being the reliance on self reported dietary surveys, which are a notoriously unreliable source of evidence.
Almost all of these Daily Mail type headlines about "the evils of fat" are based on this type of epidemiological data.
If you wanted to demonstrate a causal link between high fat and breast cancer, then you'd have to do an experimental study (ie some real science).
Experimental science involves holding one thing constant while deliberately varying another and measuring the response. In this case you'd have to take two randomly chosen sets of women and subject one to a high fat diet, and one to a conventional low-fat diet, and see how many contracted breast cancer after a number of years.
My opinion is that this type of epidemiological study is best ignored (whether the results are pro-fat or anti-fat). They only ever pick up relatively weak statistical relationships, and there are many, many examples of where these relationships are never born out by proper observational science.