No?
"Doctors regard transplants performed between identical twins very differently from those between people who do not have identical genes. Transplanting an organ between identical twins can be likened to taking tissue from one area of a person's body and putting it in another area of the body. The transplant recipient does not need antirejection drugs."
http://www.nytimes.com/2004/12/28/health/28organ.html
"Ms. Yarber had no need for antirejection drugs, because her sister was a perfect match genetically. In women who are not identical twins, drugs would be needed to prevent rejection."
http://www.nytimes.com/2005/06/08/science/08transplant.html
"1954 American doctors performed the first successful kidney transplant between identical twin brothers. No anti-rejection drugs were used."
SK Branch KFoC - HIstory of Transplantation
So that does support my belief that identical twin doesn't need anti-rejection drugs if the organ came from the other twin.
Just curious... where does it says otherwise? Link, please.