I think that the link between cardiovascular disease and inflammation is fairly well established, but the link between carbs/sugar and inflammation is less well accepted. However, I found a few papers supporting the possibility that raised blood sugar increases inflammation, at least in people with type 2 diabetes:
http://www.ncbi.nlm.nih.gov/pubmed/25456098http://www.ncbi.nlm.nih.gov/pubmed/23686079http://www.ncbi.nlm.nih.gov/pubmed/12117736Another link between obesity and inflammation and heart disease is via the effects of hormones secreted by adipose tissue on inflammation, which may create an indirect link between eating a high carb diet and inflammation (carbs being turned to fat and hence stimulating adipose tissue to release hormones such as leptin).
http://www.ncbi.nlm.nih.gov/pubmed/24936256This study in mice suggests that it could be a combination of the two:
http://www.ncbi.nlm.nih.gov/pubmed/24438079 they found that mice fed a high fat diet (which in the mouse world actually means high fat plus fairly high carb) developed significant diet-induced obesity, adipose tissue inflammation, insulin resistance, and impaired glucose tolerance compared to lean mice but that those fed high fat plus high sugar developed significantly higher inflammation in parallel with significantly increased atherosclerosis.
Fasting is known to be anti-inflammatory which might be due to the drop in blood glucose and/or its effects on leptin secretion.
So, yes, despite him being discredited at the time, it looks like he was right after all.