There has not been a single documented case of someone recovering from brain death. Articles like those posted are misleading, as they are written by persons who are not medical professionals, and frankly, have no more medical knowledge than the average person. A brain death exam is a very rigorous, clinical procedure, and many hospital policies mandate confirmatory exams. All of these patients mentioned in these dubious articles never met brain death criteria when the exam was performed. In other words, the examination was performed incorrectly.
Legally, anyone with a MD behind their name can perform a brain death exam. They could have graduated from medical school a week ago. For this reason, many hospital policies mandate the individuals that are able to perform brain death testing at that facility (i.e. one of the two people has to be a neurology attending, they have to be two separate physicians, etc.).
In short, all of the people in these questionable articles were "declared' by someone who had no business performing a brain death exam in the first place.