There is a fair amount of literature that suggests a plant based diet can be a very healthy one. Whether that has to be an all plant diet is less clear so for example there is often debate about whether vitamin B12 needs to be substituted, calcium intake etc
I just found an easy to read non technical review here about plant based diets and health . I know nothing about the authors apart from that they work for Kaiser Permanente which is one of the biggest health care insurers in the US.
.For diabetes it says
Plant-based diets may offer an advantage over those that are not plant based with respect to prevention and management of diabetes. The Adventist Health Studies found that vegetarians have approximately half the risk of developing diabetes as nonvegetarians.
19 In 2008, Vang et al
20 reported that non vegetarians were 74% more likely to develop diabetes over a 17-year period than vegetarians. In 2009, a study involving more than 60,000 men and women found that the prevalence of diabetes in individuals on a vegan diet was 2.9%, compared with 7.6% in the nonvegetarians.
17 A low-fat, plant-based diet with no or little meat may help prevent and treat diabetes, possibly by improving insulin sensitivity and decreasing insulin resistance
(of course the Adventists are known for longevity but they have a very specific lifestyle of which vegetarianism is only a part)
The doctors concerned recommend a plant based diet (including vegan, vegetarian but not exclusively, they include a Med diet for example with small amounts of animal products.)
They say towards the end, Further research is needed to find ways to make plant-based diets the new normal for our patients and employees. We cannot cure chronic diseases, but we may be able to prevent and control them by changing how we eat
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3662288/?report=reader#__ffn_sectitle
The group has obviously endorsed this to the degree that it has brought out a booklet on eating a plant based diet. (edit they do actually say that they do not necessarily endorse it at the end! )
http://www.lanimuelrath.com/wp-content/uploads/New-Plant-Based-Booklet-1214_tcm28-781815.pdf
(so as a health insurer are they trying to reduce costs associated with chronic disease ? ( of course it could be a grand conspiracy to kill of their patients

)
Just a personal anecdote but in the last year I have done a couple of Massive online courses on Nutrition. In the forums there are people who like on many on here use low carb diets but there are also very large numbers who are equally vociferous about the benefits they have seen from very low fat plant based diets.
The one thing that they would mostly all agree on though is the use of non processed foods.
I've just noticed that the booklet in fact makes quite a big stance about this so suggests getting fats for example from avocados or olives rather than seed or even olive oil)