No, BG has a lot, though not everything, to do with carbohydrates. Carbohydrates, after all, are nothing more than long strings of glucose molecules, so eating carbs automatically raises serum glucose.
It might be, however, that in the absence of dietary carbohydrate there is some mechanism that protects against damage caused by glucose. In physiological insulin resistance after ketoadaptation, for example, BG rises, but HbA1C does not. So somehow the haemoglobin in our red blood corpuscles is being protected from glycation.
It is known that high serum insulin activates genes that inhibit the body’s built-in defences against oxidation, and that β-hydroxybutyrate deactivates those genes, so perhaps it is plausible that a ketogenic diet can protect from a somewhat elevated serum glucose.
As far as insulin levels go, all food produces an insulin response, because such a response is necessary to survival. The insulin level is supposed to rise while we eat and digest, so that we can store the energy we are ingesting in our fat cells, and then it is supposed to drop between meals, so that energy can leave the fat cells and keep us going until the next meal. The problem with a high-carbohydrate diet is that it leaves insulin chronically elevated, which traps fat in the fat tissue and leads to all the other conditions associated with metabolic disease.
According to Professor Bikman, the effect of protein on insulin is not nearly as great when we don’t eat carbohydrate (or more precisely, insulin still goes up, but glucagon goes up to match—which glucagon doesn’t do, if we eat a lot of carbohydrate), and fat only ever has a bare minimum of effect on insulin, just enough to let us make use of the fat. This is why we replace carb calories with fat calories on a ketogenic diet.
In the rat and mouse studies I read, the diet given the animals was by no means what we would consider “low-carb.” It was loaded with sugar, and with polyunsaturated fats, to boot.