Not true, while milk does have low glycemic indices, it has been shown to trigger an insulin response similar to white bread. Need to look at the insulin response directly or the insulin index. Milk, even though it only has a 30 glycemic index, has a paradoxically high insulin index of 90.
Interpretation of the insulin index is still speculative at best. Here's a quote from one of the authors of the most famous and widely used insulin index studies:
"There are some instances, however, where a food has a low glycemic value but a high insulin index value. This applies to dairy foods and to some highly palatable energy-dense "indulgence foods." Some foods (such as meat, fish, and eggs) that contain no carbohydrate, just protein and fat (and essentially have a GI value of zero), still stimulate significant rises in blood insulin.
At the present time, we don't know how to interpret this type of response (low glycemia, high insulinemia) for long-term health. It may be a good outcome because the rise in insulin has contributed to the low level of glycemia. On the other hand, it may be not-so-good, because the increased demand for insulin contributes to beta-cell "exhaustion" and the development of type 2 diabetes. Until studies are carried out to answer these types of questions, the glycemic index remains a proven tool for predicting the effects of food on health."
So considering dairy's very low carbohydrate content, and insulin's purpose as a nutrient shuttle into cells, there doesn't seem to be anything wrong with using milk in this setup. Also, can you provide a link to where you found that milk has an insulin index of 90? Most every study I've found shows dairy with insulin indices around 50.
Also, considering your stance on using milk based on its disproportionate amount of carbs, I'm curious if you eat meat or eggs, as these foods have zero carb content yet they yield a disproportionately high insulin response from the body based upon the insulin index.