The short of it is that physicians do their best to apply the Harvard criteria…most of the time. Some physicians are also more liberal with determining brain death. To be clear, brain death is not reversible. Search the medical annals, you wont find a case. However, what does happen though is that someone who is not actually brain dead is mistaken to be brain dead by misapplication of criteria.
As Ubiq mentioned, the media and other low-information folks confuse the terminology and think that brain dead patients are coming back to life. Not applying criteria strictly does lead to these crazy stories we keep hearing though!