I agree with you Tim that you find all the same arguments from the vegan community as to why their diet is best for diabetes as you do from the HCLF community on here. (
On both sides you see a demonization of one nutrient or another and people become very entrenched . (just look at the replies on DD, I sigh every time I see Ancel Keys mentioned , the internet echo chamber has a lot to answer for)
People tend to read things that reaffirm their own views .
Just look at these two accounts of a recent study
The first notes that the diet wasn't really low carb so just think what a real low carb diet would do.
http://www.zoeharcombe.com/2014/09/the-low-carb-vs-low-fat-study/
The second says that at 30% it was far from a low fat diet and not very different to a SAD one. A diet of 8-12% fat is the one that has the benefits.
http://nutritionstudies.org/low-carb-hot-air/
The one systematic review that BSC doesn't mention is here
http://ajcn.nutrition.org/content/97/3/505.full
(basically, the evidence not brilliant, full of confounders and several diets have similar effects; there was not enough evidence from vegan diet) The problem I see with any randomised controlled trial is that people don't stick to the diets that they are allocated so long term trials end up with people eating much the same thing (and often not that different to where they started)
Elsewhere there have been two other papers recently that try to assess what healthy diets have in common.
Theres an account of the Katz one
here .He concludes that the best diets are ' minimally processed foods close to nature, predominantly plants'(it's now gone behind a paywall which is a pity, the
Hu one on diabetes diets is also not free access )
Both of them seem to tend towards moderation, more plant than animal, not too much of anything and very few refined foods.
Katz is actually trying to set up some sort of
coalition of people from all corners of the dietary spectrum to look for that consensus about evidenced based, healthy diet patterns to avoid (treat?) disease including T2. I'm not clear where he hopes to go with it though
He has got on board a very large group of 'luminaries' people and people with media influence, including some very well known academic researchers , people who promote diets from paleo to GI to vegan and some people more controversial (Deeprak Chopra and Mehemet Oz for example)
I don't think that I recognise anyone from the LCHF wing though . It may be that they have been asked and refused but it may also be that the methods of asking are a bit, lets say odd, or maybe I'm old fashioned but I think that such requests aren't best put on blogs or Twitter ( eg put a page search for Glimmer on this page from Peter Attia's blog
http://eatingacademy.com/cholesterol-2/random-finding-plus-pi )