It's because the bone marrow is responsible for your immune system. When you take the bone marrow from someone's body and put it into somebody else, the transplanted organ would basically "think" that it's still located in its' original body.

I guess the main reason you're asking about this is the anti-rejection medication. The DNA doesn't change after transplantation, BUT there is one way to get rid of anti-rejection pills. The bone marrow transplantation. It has to be from the same person that donated their organ as well.