An EEG cannot and does not provide conclusive evidence of brain death. Far from it. It is merely a diagnostic tool to assist a diagnosis -- the actual diagnosis of death is medically and legally dependent upon a physician. There are criteria for establishing death but they are often out of date (drowning and freezing spring to mind) and can be poorly interpreted.

They have also got it wrong before -- times too numerous to mention.

Caution is very necessary here. Its a complicated subject (legally, morally, ethically, scientifically and medically) and questions do need to be asked about organ transplant practice and ethics from time to time.