I think stories like this, about people being brought back from the dead, fuel unease about posthumous organ donation. People quite reasonably worry that, if they register as donors, they will be left for dead, when they could have been saved/revived.
It's worth emphasising that the story here is about cardiac death ("Most people regard cardiac arrest as synonymous with death, he says. But it is not a final threshold"). The definition of death used for organ donation is brain death. As the article goes on to say, "[Dr Jerry] Nolan stops short of saying that Carol was brought back from the dead. Hospitals do not declare death, he says, until they have ruled out all processes that can be reversed."
Nonetheless, this article serves to highlight the ambiguity and confusion surrounding death. Of course, public misunderstanding is somewhat to be expected, given current medical practice - e.g. the family may be informed that, since their relative is [brain] dead, doctors intend to turn off life support, in order to 'let them die'.
In the words of Dr Nolan, as quoted in the article, "We used to think death was a sort of sudden event - we stop the oxygen going to the brain and after a few minutes that was that. But actually, we know that the dying process at the cellular level goes on for a period of time". Our understanding of, and attitudes towards, death and dying are obviously crucial for organ donation (provided, of course, we continue to accept the assumption that it is only permissible to take organs from the dead, except in special circumstances).