Why will tissue from identical twin be rejected in some cases?
This was too long for a comment, but I have absolutely no evidence for what I'm about to say :)

It looks like that sentence was a little bit of hand-waving, as the author didn't want to categorically state that identical twin tissue would never be rejected. I suspect that in the early days there may have been reports of organ failure (esp. kidneys) in the recipient that were incorrectly identified as rejection episodes. I suppose there's also the slight possibility that one twin could have a mutation event very shortly after the separation of the twins in utero (when all the cells are still pluripotent) that could somehow change or (more likely) silence one or more of the HLA or other surface antigens involved in transplant rejection. This would almost certainly have to happen when the separated twin was a single cell. The mutated twin would therefore not express an antigen the non-mutated twin did, and if the non-mutated twin donated a kidney or other organ to the mutated one, its immune system wouldn't recognize the silenced antigen and could potentially result in rejection.

Like I said earlier, all pure conjecture :)