I haven't seen that study, and frankly I think there are too many variables to draw a blanket conclusion about fat. For instance, what kind of fat was predominant in the diet? Did the high fat subjects gain body fat, which contributes to estrogen levels, and other hormones?
Were the fats organic, or were they from non-organic food sources, in which case they were probably loaded with all sorts of goodies from bovine growth hormone to dioxin?
Generally, indiscriminate high fat diets have some bad health effects. We tend to concentrate here on their impact on our physique in a high carb/low fat vs. low carb/higher fat type discussion, but fat (generally, not specific types or from specific sources) is a culprit in a number of health problems (as are simple carbs, for that matter).
The ratio of omega-3 to omega-6 fats might matter, so the study would need to not be feeding too much of the latter or it might simply be that a diet high in certain fats is the culprit but not all fats.
There are studies that implicate the importance of the ratio of inflammatory (omega-6 fats are usually what's tested) fats to anti-inflammatory (omega-3, usu. fish oil) fats in cancer progression.
For instance, if you have cancer cut the fat generally, but dramatically increase the fish oil, as most fats are slightly inflammatory while omega-3 fats are anti-inflammatory. Inflammation is one of the means by which cancer cells metastasize and invade.
While I haven't seen any studies on this phenomenon contributing to the development of cancers, it is logical that it would have an impact at least in some kinds of cancers. Our bodies are developing pre-cancerous conditions all the time, but our defenses deal with these before they become full-blown cancer.
Anything that gives the pre-cancerous and individual cancer cells an edge in resisting and multiplying would seem to logically increase the likelihood that we develop a cancer. Again, I haven't seen any studies on this.
To Headhunter's comment re doctors being down on milk and meat, I don't think they are down enough on them. Eating meat and milk products produced by our current food industry is high on the list of risky behaviors. It isn't necessarily the milk or the meat per se, but how the animals are raised, and what they are fed and injected with.
We know from basic science that eating up the food chain gets you a healthy dose of whatever bad stuff humans dump into the environment through a process called bio-accumulation.
Add to that the hormones, anti-biotics, corn (which makes cows very unhealthy but bigger), all sorts of inappropriate foods (like feeding cow rendered cow parts) in feed, and living in too close proximity, and you have a recipe for highly tainted food.
While this isn't the only culprit for higher cancer rates (I can list dozens), it seems prudent to limit eating up the food chain and to avoid non-organic products especially when they are high in animal fats that store a lot of the bad stuff the animals are exposed to. Again, it is not the fat per se, but what's in the fat that seems the bigger concern.
Of course some fats are good cancer fighters. Fish oil being the most prominent among them. Just make sure that your fish oil is tested and certified to be free of heavy metals and/or purified. Flax seed oil is a bit more problematic, as it has been implicated in prostate problems.
It is probably safe to take a very small amount of flax seed oil for men in a multi-good fat supplement (like Udo's Choice), but men should avoid flax seed oil generally, and rely on fish oil for their essential fatty acid supplements.
And no, I'm not a doctor. Just someone with too much education who has had too much cancer in my family of recent (lost my father & sister-in-law last year and now have a mother-in-law battling cancer) and has had cancer myself, and had a strong incentive to read extensively in the medical literature on the subject.