Correct. They brew the sulfur out of it along with the lube. They then add some kind of lube to it (hopefully)! I believe some stations (Pacific Pride?) then document each delivery with a sample test to insure the lube was added. Without that added lube diesels would be littering our highways.
X2 Sulphur is acidic... north American diesel fuel winter blends are produced by blending a percentage of #1 kerosene with #2 to achieve a CFPP for the different ambient temperatures in the various regions. (CFPP - cold filter plugging point). Or, as most fuel suppliers do, produce winter fuel using additives as it is cheaper. Now for Arctic regions, winter fuel... that's another story, lots of blending there.
p.s. never used any "off the shelf" additives in my diesels.