Normally it seems accepted that the stem cells tend to be killed by the immune system or die simply because they are in a strange environment away from their requirements. in the past some local stem cell injections were tried and succeeded but later on was found that the stem cells were very few and worked (or in part worked) because of all the rest that went into the injection recreating a fake environment that fooled the stem cells into believing that they were in the right place. the rest is down to the legislation, with modern techniques and the knowledge we now have, nobody is risking anyone health into using untested stem cells therapies that haven't passed the required quality issues related with injecting a foreign body into the patient
Because the expression of MHC molecules of cells in culture were modified and because the peptides presented these MHC molecules were different from those in the human body. The cells are just killed by NK cells.