My understanding, from everything I have read and heard, is that there is still a chance of Graft vs Host Disease (i.e. rejection) even from just pure cord blood cells, with all the other blood components removed.
I was at a clinic awhile back preparing to get a cord cell treatment, and ended up declining treatment there, and left.
This was one of the main reasons that I decided not to have a treatment using cord blood cells.
The doctor there told me that they generally keep at least 3 different "batches" of cord blood cells at their clinic. What they do is to take a small amount of your blood, and combine it with the 3 (or more) cord blood cell samples. Then they leave the combination in test tubes for a day or so, and check them under a microscope. Whichever batch has the least cellular reaction going on of the 3 batches is the one that they use to inject into the patient! I found this to be a somewhat lame practice, and perhaps other clinics do it differently.
Perhaps there is a way to have zero risk of graft vs host disease, or perhaps there will be in the further evolution of cord blood-based treatments.
Graft vs host disease is a very nasty syndrome. Very basically, your blood cells are very upset, and are fighting it out with the "alien" cells.
I have heard some of the early folks who went to Mexico for treatment (such as Barbara) describe very bad reactions to cord-blood cell treatment.
One thing is for sure: stem cells and any blood components either come from your own blood or some cells in your body, or they come from someone else.
I have chosen to use only my own cells to this point.
Obviously, if a child or adult is dying of cancer or leukemia, you take whatever risks exist if a matched sibling or other donor can not be found.
Maybe a doctor will chime in to add to this and/or correct me?