I don't think (although i stand ready to be corrected) that all milk is skimmed at the dairy and then the fat is put back. The reason that there is more sugar in skimmed milk than whole milk or semi skimmed is because skimming reduces the total volume of the milk, NOT because "they" add more sugar.
for example, lets say that in 10 fluid ounces of whole milk, there is one fluid ounce of fat and one fluid ounce of sugar. If you remove the fat, you end up with nine fluid ounces of liquid. In order to get back to your ten fluid ounces, you have to add more skimmed milk containing its sugar and that additional one fluid ounce will contain 0.1 fluid ounces of sugar so the total amount of sugar in 10 fluid ounces of skimmed milk will be 1.1 ounces.
Of course the figures aren't that easy and rounded, I just chose them to make the example easy to follow cos it took me 3 tries before I got it!