I would imagine that if this is true then it would be HIGHLY dependent on what type of carbs are normally consumed in the diet. Processed wheat flour products and sugar are surely not going to increase lifespan.
Another thing we have to consider is half of Americans are pre-diabetic (insulin resistant) and there is a similar rate of obesity. Carbohydrate overfeeding is certainly a causative factor in this, but not necessarily the only one.
Consuming a high-carbohydrate diet in the context of insulin resistance is going to frequently cause higher than normal insulin level in blood. This is also not good for longevity/cancer/inflammation, etc.
There can still be room for carbohydrates in this context but I question whether it's optimal for insulin resistant individuals to consume high-carb diets.
Nice tips on some of those substitutions!