“Brain dead” versus “physically dead”: it’s all just semantics, right?

By way of the Associated Press’ breaking coverage of Palestinian leader Yassir Arafat’s death-but-not-death, it’s come out that:

French television station LCI quoted an anonymous French medical official as saying Arafat was in an “irreversible coma” and “intubated” – a process that usually involves threading a tube down the windpipe to the lungs. The tube is often connected to a life support machine to help the patient breathe.

In other words, “brain dead, but not physically shut down.”
Cursed word games! It’s much like trying to pick apart the distinction between, say, a “security fence” and an “imprisoning wall“.