Does the China Study prove milk causes cancer?

The China Study has sold over 500,000 copies making it one of the best selling nutrition books in history. It purports to prove that there is a connection between meat and dairy consumption and a variety of diseases including cancers of the breast, prostate, and large intestine. Animal products are also accused of contributing to diabetes, heart disease, obesity, autoimmune disease, osteoporosis, degenerative brain disease, and macular degeneration. Only 39 of the 350 pages in the book are actually devoted to the China Study.
The study was conducted by T. Colin Campbell and was influenced by the Seventh Day Adventist background of the authors. One flaw of the study is that those eating a plant based diet in China were consuming a lower calorie count that those eating meat. It is a long known fact that fasting in any form prolongs life and reduces and delays the development of a wide variety of diseases. A plant based diet does decrease caloric intake due to the high fiber intake. Plants also provide a wide variety of phytonutrients which protect from disease.
Many animal products today are produced by feeding animals grains resulting in excessive fattening of the animals and excessive levels of omega-6 fatty acids. Historically, many people have lived long and healthy lives consuming primarily animal products. These products were, however, superior nutritionally to many of the animal products consumed today. Most milk products, for example, are pasteurized today. Historically this was rare. The casein which Campbell focuses on can be produced with both low and high temperature processes. The high-temperature spray-drying process is known to create carcinogens. Campbell neglects to mention that high-casein diets protected rats from cancer when fed casein before or during the aflatoxin dosing rather than after.
Another flaw of the study is that consumption of refined carbohydrates is ignored, despite the fact that meat eaters usually have a higher income and can afford more refined foods. The data of the China Study itself suggests that sugar and soluble carbohydrate have seven times the magnitude of correlation with cancer that animal protein intake does.