OK, now there is a link to the main body of the study and I can get a better understanding.
Problem number one, the population was scored using percentage of energy eaten of carbs, protein, and fat. Then the scored people were divided into 10 groups, aka deciles. The problem here is that you could be put in the lowcarb group even if you are eating a ton of carbs, as long as you are eating a larger percentage of calories as fat and protein. This is not really low carb. In fact, the LOWEST decile group of carb consumption was eating a mean intake of 116.7 grams of carb per day. This is not super low carb compared to what paleo typically advocates. In fact, it's probably on the higher side of what most paleos eat. Most people in the low carb group were probably not actually low carb at all, at least not according to Atkins or paleo standards. In fact, some people in the lowest carb decile group may well have been eating way more carbs than some people in the high carb groups! For instance, I could eat a steak and a banana and be in the same carb group quintile as someone who ate 10 steaks and 10 bananas. Or someone who ate 10 steaks and nine bananas would be considered in a lower carb group than me, even though they at 9 times more carb than I did.
The researchers also say they did not consider overall caloric intake levels in any of their multivariate analysies. So they did not control for true lowcarbness or calories in the more robust type of statistical analysies. They do mention they did control for caloric intake in 'secondary analysis' but I couldn't find any further details on that or how or when they did it.
OK, so now on to their stastical results. Much of their results was not statistically significant. COnfidence intervals do not mean much as far a I can tell and are not indicative of statistical significance. What you need to look for is a P value of less than .05 . If it's not smaller than .05, then it is not statistically significant and therefore could be more easily due to chance variation. Much of their correlations do not meet that standards of statistical significance.
Interestingly, in a subgroup of individuals that had blood lipids tested, no correlation was found between total cholesterol, HDL, and LDL. So at least they can't argue that low carb is bad for blood lipids. Also, a statistically significant correlation was found between higher carb (as percentage of calories) intake and triglycerides in the blood. No surprise for us paleo eaters there. Carbs are predictable strong risers of trigs in the blood and this shows even in their weird carb scoring system.
They found no statistical diffs correlated with level of animal fat consumption as percentage of calories.
They did find a statistical correlation between increased vegetable fat consumption and lessening of heart disease. They talk about this in a few places, but then buried further down in discussion, they say "only vegetable protein was associated with a significantly reduced risk [of coronary heart disease] in age-adjusted analyses , and this association became nonsignificant in multivariate analyses. So in other words, when they crunched the numbers to control for confounding factors, the correlation between consumption of vegetable fat as percentage of calories and reduced risk of coronary heart disease disappears. THerefore, they are misleading you when they say they insinuate they found a true correlation. They also never directly compare animal fat low carb groups with veg fat low carb groups, so it's hard to say how they directly compare. However, I think at no point do they give us any real evidence that when proper multivariate analysis is used, there is any statistically significant differences between animal and veg fat intake as percentage of calories as compared with any health issues.
ANyway, I think the main point here, when concerned with our own beliefs about eating healthy and eating lower carb, is that they did not truly group people according to actual carb intake according to amount of carbs actually put into the mouth and eaten, and I think that is the biggest flaw in this study. The second would be insinuating an advantage to plant fat intake even though said statistical significance disappears when more robust statical methods are used.
In fact, I don't think this study tells us much if anything about low carb eating because as far as I can tell, only one of the 10 quintiles was even close to being actually low carb.