To clarify what I said, some dairies take skim milk, “fortify” it with powdered milk, which boosts it protein level and improves its appearance, then adds butterfat to get a standard 1% or 2% milk. It does create a reconstituted taste, however, though it is only partly reconstituted.
This is accompanied by other processes, such as homogenization to break up larger fat globules, high temperature (HTST) processing, the “fortification” with either water or fat soluble vitamins. De-aeration of the milk prior to the addition of iron compounds was also found to reduce flavor problems. Calcium fortificant preparations including stabilisers and emulsifiers have been used for this purpose to maintain calcium in suspension so as to improve mouthfeel and appearance of products.
You were right about the blue dye, which was discontinued some years ago.
All milk that comes into the dairy facility is skimmed. The reason is that butterfat content is not consistent from cow to cow. One tanker may have 5% butterfat and another may only have 3.4%. After that is done the milk is pasteurized and homogenized to have 3.9% 2% 1% 1/2% cream and Fat Free. No dye is added as you noted.
For fat free and flavored milk, milk powder is added along with the flavor to give the milk a higher protein level and to thicken it.
You stated that "a lot of milk today is reconstituted from dehydrated" and it isn't, "with fat added for flavor" is a odd way of saying that the cream is put back in, and of course as you noted your "blue dye for whiteness." is more then a bit out of date.
You spun, you got called.