The study says refined carbs are bad — that's an important distinction. Also, some research (The China Study, for example) suggests that proteins (not fat) from animal-based foods are a cause of heart disease (and cancers).
Sorry, you're right about the refined carbs. Also, going further along the meat lines, there was also recent research differentiating processed meats (e.g. bacon, sausage, lunch meats, etc.) versus unprocessed meats. If I remember correctly, the unprocessed meats had no real links to heart disease and cancers (in moderation). However, the processed meats did show some links to those health problems. The researchers speculated that it was probably either the high salt content or the nitrates in the processed meats that were the culprits, but the study didn't actually look at that.