I stopped reading at the end of that obviously fake anecdote, how much credibility can the rest of the article have if they actually believe that story.
The doctors don't believe the story. The woman does. The doctors believe that the woman's belief caused her early death, but that's independent of whether they accept that story as true - people (the woman) can convince themselves of a lot of things.
You're absolutely right. However, I'm still struggling to believe that the woman existed at all, the entire story just sounds so made up.