Torchwood Dead Man Walking: Technically, shouldn't Death have had killed enough people?

Gwen says that Death needed to kill 13 times before it had a permanent
hold...Didn't Jack's death count? Death "killed" Jack when it first
came out of Owen, so technically wouldn't that have meant that it
killed 13 times, and so should have had a permanent hold? It killed 12
times in the hospital. Or didn't Jack's death count?